Exhibit 99.1

Company announcement — No. 36 / 2019

Total number of shares and voting rights in Zealand Pharma at September 30, 2019

Copenhagen, September 30, 2019 — Zealand Pharma A/S (“Zealand”) (NASDAQ: ZEAL) (CVR-no. 20 04 50 78), a Copenhagen-based biotechnology company focused on the discovery and development of innovative peptide-based medicines, in accordance with Section 10 of the Danish Statutory Order on Issuers’ Disclosure Obligations, announces the total number of shares and voting rights in the Company at the end of a calendar month during which there have been changes to its share capital.

In Company announcement No. 33/2019 of September 11, 2019, Zealand announced an increase in share capital relating to the completion of a private placement and directed issue of new shares, and in No. 34/2019 of September 13, 2019, Zealand announced an increase in its share capital relating to the exercise of employee warrants. Following these announcements, the table below lists the total number of shares and voting rights in Zealand at September 30, 2019:

Date	Number of shares (nominal value of DKK 1 each)	Share capital (nominal value in DKK)	Number of voting rights
September 30, 2019	35,865,461	35,865,461	35,865,461

For further information, please contact:

Emmanuel Dulac, President and Chief Executive Officer

Tel.: +45 50 60 36 36, e-mail: edu@zealandpharma.com

Lani Pollworth Morvan, Investor Relations and Communication

Tel.: +45 50 60 37 78, e-mail: 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 focus on specialty gastrointestinal and metabolic diseases. Zealand’s portfolio also includes two clinical license collaborations with Boehringer Ingelheim and pre-clinical license collaboration with Alexion Pharmaceuticals.

Zealand is based in Copenhagen (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.