Exhibit 99.1

Company announcement — No. 40 / 2019

Notification of managers and closely related parties’ transactions with Zealand Pharma shares in connection with employee warrant program

Copenhagen, November 27, 2019 — Pursuant to the Danish Securities Trading Act, section 28a, Zealand Pharma A/S (“Zealand”) (NASDAQ: ZEAL) (CVR-no. 20 04 50 78) discloses information on transactions with the company’s shares and related securities by managers and persons/companies closely related to them.

With reference to the above, Zealand announces that it has received information on transactions for disclosure. Please see the attached files.

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 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.