• Monarch – Christian X^[1]
• Prime minister – Niels Neergaard (until 24 April), Thorvald Stauning

• 22 January – the 1924 Faroese general election is held.
• 11 April – the 1924 Danish Folketing election is held.
• 23 April – the Stauning I Cabinet is formed following the Folketing election.
• 18 July – Tisvildeleje railway station opens.
• 1 August – the Institut Jeanne d'Arc is established in Frederiksberg.
• August 9–17 – the 2nd World Scout Jamboree is held in Ermelunden, Denmark.

• 15 June – The opening match of the first Nordic Football Championship is held at Københavns Idrætspark. The Swedish national team defeats the Danish team 3–2.
• 5–27 July – Denmark competes at the Summer Olympics, winning 9 medals in addition to several medals from the art competition.
• 23 July – Esbjerg fB is founded.

Date unknown edit

• B 1903 wins their second Danish football championship by defeating B 1913 5–0 in the second replay of the final of the 1923–24 Danish National Football Tournament (after two 1–1 draws).

January–March edit

• 7 January – Karen Strand, silversmith (died 2000)

April–June edit

• 24 June – John Hansen, football player (died 1990)

July–September edit

• 18 July – Inge Sørensen, swimmer (died 2011)
• 14 August – Holger Juul Hansen, actor (died 2013 in the United States)

October–December edit

• 10 November – Klaus Baess, Olympic sailor (died 2018)
• 20 November – Karen Harup, swimmer (died 2009)
• 29 November – Erik Balling, TV and film director (died 2005)
• 2 December – Else Marie Pade, composer (died 2016)
• 7 December – Bent Fabricius-Bjerre (a.k.a. Bent Fabric), composer, pianist (died 2020)
• 29 December – Gurli Vibe Jensen, missionary, priest and writer (died 2016)^[2]

• 18 March – Walter Christmas, author (b. 1861)
• 12 April – Frederik Levy, architect (born 1851 in Germany
• 17 May – Niels Peter Bornholdt, businessman (born 1842)
• 19 September – Hannibal Sehested, prime minister of Denmark (b. 1842)
• 7 December – Rudolph Sophus Bergh, composer (b. 1859)