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

• 9 April – Operation Weserübung takes place, beginning the occupation of Denmark by Nazi Germany.^[2]
• 16 April – Princess Margrethe, the future Queen Margrethe II, is born to Crown Prince Frederik and Crown Princess Ingrid of Sweden.

Badminton edit

• 7 November – Lillerød Badminton Club is founded in Lillerød

Football edit

• Kjøbenhavns Boldklub wins their eighth Danish football championship by winning the 1939–40 Danish Championship League.

January–March edit

• 12 January – Helle-Vibeke Erichsen, artist and illustrator (died 2016)
• 14 February – Eva Sørensen, sculptor and ceramist (died 2019)
• 17 February – Julius Paulsen, painter (born 1880)
• 25 February – Thue Christiansen, greenlandic politician (died 2022)
• 29 March – Allan Botschinsky, jazz trumpeter (died 2020)

April–June edit

• 16 April – Princess Margrethe, the future Queen Margrethe II^[3]
• 21 April – Erik Hagens, painter and illustrator

October–December edit

• 24 October – Jørgen Boberg, painter and illustrator (died 2009)
• 3 December – Palle Jacobsen, ballet dancer (died 2009)

January–March edit

• 28 January – Heinrich Dohm, painter of portraits, genre works and religious paintings (born 1875)
• 13 March – Gustav Frederik Holm, Arctic explorer, naval officer (born 1849)
• 28 March – Henrik Grønvold, painter (born 1858)
• 25 May – Marie Krøyer, painter (born 1867)

July–September edit

• 27 July – Gerda Wegener, painter (born 1886)

October–December edit

• 10 December – Christian Schrøder, film actor (born 1869)
• 19 December – Charlotte Norrie, nurse and women's rights activist (born 1855)^[4]