6-K

UNITED STATES

SECURITIES AND EXCHANGE COMMISSION

Washington, D.C. 20549

FORM 6-K

REPORT OF FOREIGN PRIVATE ISSUER

PURSUANT TO RULE 13a-16 OR 15d-16

UNDER THE SECURITIES EXCHANGE ACT OF 1934

April 6, 2020

Commission File Number: 001 - 38178

Zealand Pharma A/S

(Exact Name of Registrant as Specified in Its Charter)

Sydmarken 11

2860 Søborg (Copenhagen)
Denmark

(Address of principal executive offices)

Indicate by check mark whether the registrant files or will file annual reports under cover of Form 20-F or Form 40-F.

Form 20-F x            Form 40-F ¨

Indicate by check mark if the registrant is submitting the Form 6-K in paper as permitted by Regulation S-T Rule 101(b)(1): ¨

Indicate by check mark if the registrant is submitting the Form 6-K in paper as permitted by Regulation S-T Rule 101(b)(7): ¨

Furnished as Exhibit 99.1 is a company announcement of Zealand Pharma A/S or the Company, dated April 6, 2020, announcing the receipt of a major shareholder notification from Wellington Management Group LLP. Furnished as Exhibit 99.2 are additional details provided by the shareholder.

SIGNATURE

Pursuant to the requirements of the Securities Exchange Act of 1934, the registrant has duly caused this report to be signed on its behalf by the undersigned, thereunto duly authorized.

Zealand Pharma A/S
By:	/s/ Matthew Dallas
	Name:	Matthew Dallas
	Title:	Chief Financial Officer

Date: April 6, 2020

2

EXHIBIT INDEX

Exhibit No.	Description
99.1	Company announcement dated April 6, 2020
99.2	Details of major shareholder announcement: Wellington Management Group LLC

3

EX-99.1

Exhibit 99.1

Company announcement – No. 17 / 2020

Zealand Pharma major shareholder announcement: Wellington Management Group LLP

Copenhagen, April 6, 2020 – Zealand Pharma A/S (“Zealand”) (NASDAQ: ZEAL) (CVR-no. 20045078), a Copenhagen-based biotechnology company focused on the discovery and development of innovative peptide-based medicines, announces the receipt of the following major shareholder notification:

From April 1, 2020, Wellington Management Group LLP indirectly hold a total of DKK 1,790,560 shares and financial instruments with similar economic effect according to section 39(2)(2) of the Danish Capital Markets Act in Zealand (1,777,275 shares corresponding to 4.81% of the total share capital of the Zealand, and 13,285 financial instruments corresponding to 0.04% of the total share capital of the Zealand) and a total of 1,777,275 voting rights (each share carrying one vote) in Zealand corresponding to 4.85% of the total share capital and voting rights of Zealand. Additional details on the financial instruments with similar economic effect is included in the attachments to this announcement.

The shares, financial instruments with similar economic effect according to section 39(2)(2) of the Danish Capital Markets Act and voting rights in Zealand are directly held by Wellington Management Company LLP and Wellington Management International Ltd.

Wellington Management Company LLP is a direct controlled undertaking of Wellington Investment Advisors Holdings LLP which, in turn, is a direct controlled undertaking of Wellington Group Holdings LLP which, in turn, is a direct controlled undertaking of Wellington Management Group LLP.

Wellington Management International Ltd is a direct controlled undertaking of Wellington Management Global Holdings, Ltd which, in turn is a direct controlled undertaking of Wellington Investment Advisors Holdings LLP which, in turn, is a direct controlled undertaking of Wellington Group Holdings LLP which, in turn, is a direct controlled undertaking of Wellington Management Group LLP.

For further information, please contact:

Zealand Pharma Investor Relations

+45 50 60 38 00 investors@zealandpharma.com

Lani Pollworth Morvan, Investor Relations and Communication

lpm@zealandpharma.com

About Zealand Pharma A/S

Zealand Pharma A/S (Nasdaq Copenhagen and New York: ZEAL) ("Zealand") is a biotechnology company focused on the discovery and development of innovative peptide-based medicines. More than 10 drug candidates invented by Zealand have advanced into clinical development, of which two have reached the market. Zealand’s current pipeline of internal product candidates focuses on specialty gastrointestinal and metabolic diseases. Zealand’s portfolio also includes clinical license collaboration with Boehringer Ingelheim and a pre-clinical license collaboration with Alexion Pharmaceuticals.

Zealand is based in Søborg, Denmark. For further information about the company's business and activities, please visit www.zealandpharma.com or follow Zealand on LinkedIn or Twitter @ZealandPharma.

EX-99.2

Exhibit 99.2

Opdateret 06-02-2018 Standard form for notification of major holdings % % Total share capi-1 6. Total positions of person(s) subject to the notification obligation: Voting rights: Voting rights attached to shares in % (total of 7.1.A) Voting rights through fi-nancial instruments in % (total of 7.1.B.1 + 7.1.B.2) Total of both in (7.1.A + 7.1.B) Total number of voting rights of issuervi Resulting situation on the date on which threshold was crossed or reached 4.81% 0.04% 4.85% 36,887,952 Positionofprevious notification (if applicable) 5.02% 0.04% 5.06% Share capital: Share capital attached to shares in % (total of 7.2.A) Sharecapitalthrough financial instruments in % (total of 7.2.B.1 + 7.2.B.2) Total of both in (7.2.A + 7.2.B) tal in issuervi Resulting situation on the date on which threshold was crossed or reached 4.81% 0.04% 4.85% 36,887,952 Positionofprevious notification (if applica-ble) 5.02% 0.04% 5.06% 1. Identity of the issuer or the underlying issuer of existing shares to which voting rights are attachedi: ZEALAND PHARMA A/S 2. Reason for the notification (please tick the appropriate box or boxes): ☒ An acquisition or disposal of voting rights or share capital ☐ An acquisition or disposal of financial instruments ☐ An event changing the breakdown of voting rights or share capital ☐ Other (please specify)ii: 3. Details of person subject to the notification obligationiii: Name: Wellington Management Group LLP City and country of registered office (if applicable): 280 Congress Street, Boston, MA, 02210 USA 4. Full name of shareholder(s) (if different from 3.)iv: N/A 5. Date on which the threshold was crossed or reachedv: 1st April 2020 NOTIFICATION OF MAJOR HOLDINGS (to be uploaded at http://oasm.finanstilsynet.dk)

2 7.2. Notified details of the resulting situation on the date on which the threshold was crossed or reached: 7.1.B.2: Financial Instruments with similar economic effect acc. to Sect. 29 (4)(2) of Securities Trading, etc. Act Typeof financial instrument Expiration dateviii Exercise/ conversion periodix Physicalor cash settlementx Numberof voting rights % of voting rights Equity Swap 15 May 2020 21 Aug 2019 - 15 May 2020 Cash settlement 10,364 0.03% Equity Swap 15 May 2020 05 Oct 2018 - 15 May 2020 Cash settlement 852 0.00% Equity Swap 05 May 2020 02 Jul 2018 - 05 May 2020 Cash settlement 582 0.00% Equity Swap 15 May 2020 13 Jul 2018 - 15 May 2020 Cash settlement 528 0.00% Equity Swap 15 May 2020 05 Apr 2018 - 15 May 2020 Cash settlement 502 0.00% Equity Swap 15 May 2020 14 Sep 2018 - 15 May 2020 Cash settlement 245 0.00% Equity Swap 15 May 2020 09 Jul 2018 - 15 May 2020 Cash settlement 212 0.00% SUBTOTAL 7.1.B.2 13,285 0.04% 7.1.B.1: Financial Instruments according to section 29 (4)(1) of the Securities Trading, etc. Act Typeof financial instrument Expiration dateviii Exercise/ conversion Periodix Number of voting rights that may be acquired if the instru-ment is exercised/converted. % of voting rights SUBTOTAL 7.1.B.1 7.1. Notified details of the resulting situation on the date on which the threshold was crossed or reached: 7.1.A: Voting rights attached to shares Class/typeof shares ISIN code (if possi-ble) Number of voting rightsvii % of voting rights Direct (Sect. 29 (1) of Securities Trading, etc. Act) Indirect (Sect. 29 (3) of Securities Trading, etc. Act) Direct (Sect. 29 (1) of Securities Trading, etc. Act) Indirect (Sect. 29 (3) of Securities Trading, etc. Act) DK0060257814 1,777,275 4.81% SUBTOTAL 7.1.A 1,777,275 4.81%

capital 3 7.2.B.2: Financial Instruments with similar economic effect acc. to section 29 (4)(2) of the Securities Trading, etc. Act Type of financial instrument Expiration dateviii Exercise/ conversion periodix Physical or cash settlementx Numberof shares % of share capital Equity Swap 15 May 2020 21 Aug 2019 - 15 May 2020 Cash settlement 10,364 0.03% Equity Swap 15 May 2020 05 Oct 2018 - 15 May 2020 Cash settlement 852 0.00% Equity Swap 05 May 2020 02 Jul 2018 - 05 May 2020 Cash settlement 582 0.00% Equity Swap 15 May 2020 13 Jul 2018 - 15 May 2020 Cash settlement 528 0.00% Equity Swap 15 May 2020 05 Apr 2018 - 15 May 2020 Cash settlement 502 0.00% Equity Swap 15 May 2020 14 Sep 2018 - 15 May 2020 Cash settlement 245 0.00% SUBTOTAL 7.2.B.2 13,285 0.04% 7.2.B.1: Financial Instruments according to section 29 (4)(1) of the Securities Trading, etc. Act Type of financial instrument Expiration dateviii Exercise/ conversion periodix Number of shares that may be acquired if the instrument is exercised/converted. % of share SUBTOTAL 7.2.B.1 7.2.A: Share capital attached to shares Class/typeof shares ISIN code (if possi-ble) Number of sharesvii % of share capital Direct (Sect. 29 (1) of Securities Trading, etc. Act) Indirect (Sect. 29 (3) of Securities Trading, etc. Act) Direct (Sect. 29 (1) of Securities Trading, etc. Act) Indirect (Sect. 29 (3) of Securities Trading, etc. Act) DK0060257814 1,777,275 4.81% SUBTOTAL 7.2.A 1,777,275 4.81%

equals or is higher Done at London, UK on 2nd April 2020 4 10. Additional informationxiv: Wellington Management Company LLP is a direct controlled undertaking of Wellington Investment Advisors Holdings LLP which, in turn, is a direct controlled undertaking of Wellington Group Holdings LLP which , in turn, is a direct controlled undertaking of Wellington Management Group LLP. Wellington Management International Ltd is a direct controlled undertaking of Wellington Management Global Holdings, Ltd which, in turn is a direct controlled undertaking of Wellington Investment Advisors Holdings LLP which, in turn, is a direct controlled undertaking of Wellington Group Holdings LLP which , in turn, is a direct controlled undertaking of Wellington Management Group LLP. 9. In case of proxy voting: [name of the proxy holder] will cease to hold [% and number] voting rights as of [date] 8. Information in relation to the person subject to the notification obligation (please tick the applicable box): ☐ Person subject to the notification obligation is not controlled by any natural person or legal entity and does not control any other undertaking(s) holding directly or indirectly an interest in the (underlying) issuerxi. ☒ Full chain of controlled undertakings through which the voting rights and/or the financial instruments are effectively held starting with the ultimate controlling natural person or legal entityxii: Namexiii % of voting rights if it equals or is high-er than the notifia-ble threshold % of voting rights through financial in-struments if it equals or is higher than the notifi-able threshold Total of both if it than the notifiable threshold Wellington Management Group LLP Wellington Group Holdings LLP Wellington Investment Advisors Holdings LLP Wellington Management Company LLP Wellington Management Group LLP Wellington Group Holdings LLP Wellington Investment Advisors Holdings LLP Wellington Management Global Holdings, Ltd. Wellington Management International Ltd

[LOGO]