• Monarch – Christian X^[1]
• Prime minister – Thorvald Stauning

• 18 May – The state national police force Rigspolitiet – under command of one chief of police – begins operations.^[2]
• 26 September – The Storstrøm Bridge is inaugurated.
• 14 December – Many documents from the National Archives of Denmark, the Royal Danish Library and Copenhagen University Library relating to Norwegian conditions are transferred to Norway.^[2]

Cycling edit

• 21–29 August – The 1937 UCI Track Cycling World Championships are held in Copenhagen.
• Kees Pellenaars (NED) and Frans Slaats (NED) win the Six Days of Copenhagen six-day track cycling race.

Football edit

• AB wins their third Danish football championship by winning the 1936–37 Danish Championship League.

January–March edit

• 14 January – Erland Kops, badminton player (died 2017)
• 1 February – Anders Bodelsenm author (died 2021)
• 23 March Helge Rode, writer, critic and journalist (born 1769)

April–June edit

• 14 June – Jørgen Leth, film director, writer, poet

October–December edit

• 3 December – Søren Krarup, pastor, writer and politician (died 2023)
• 14 December – Aino Kann Rasmussen, h archaeologist, curator
• 29 December – Ursula Munch-Petersen, ceramist

• 8 February – Martin Borch, architect (born 1852)
• 22 March – Thorvald Aagaard, composer (born 1877)
• 23 March – Helge Rode, writer, critic and journalist (born 1870)
• 30 December – Hans Niels Andersen, businessman, founder of East Asiatic Company (born 1852)