• Monarch – Christian X^[1]
• Prime minister – Niels Neergaard

• May – The departure of the 5yh Thule Expedition.

• 30 March – Lyngby Boldklub is founded.
• 21 August – Gentofte-Vangede Idrætsforening is founded.

Cycling edit

• 30 July – 8 August – The 1921 UCI Track Cycling World Championships are held in Copenhagen.
  • Henry Brask Andersen wins gold, Erik Kjeldsen wins silver and Johan Normann wins bronze in men's sprint at the Amateur event.
• 4 August – The 1921 UCI Road World Championships are held in Copenhagen
  • Willum Nielsen wins silver in Men's amateur road race.

Football edit

• AB wins its second Danish football championship by defeating Aarhus Gymnastikforening 3–0 in the final of the 1920–21 Danish National Football Tournament.

January–March edit

• 14 March – Lis Hartel, equestrian athlete (died 2009)
• 16 March – Jens Bjerre, Danish author, filmmaker and explorer (died 2020)

April–June edit

• 28 May – Kay Werner Nielsen, cyclist (died 2014)
• 29 May – Karen Hoff, canoeist (died 2000)
• 11 June – Ib Spang Olsen, artist and illustrator (died 2012)

July–September edit

• 1 September – Simon Spies, businessman, billionaire (died 1984)

October–December edit

• 21 November – Margrethe Schanne, ballerina (died 2014)
• 27 November – Ole Sarvig, poet (died 1991)

January–March edit

• 2 February – Antonio Jacobsen, painter (born 1759)
• 12 February – Troels Frederik Lund, historian (born 1840)

April–June edit

• 18 May – Martin Nyrop, architect (born 1849)

July–September edit

• 8 September – Ingeborg Raunkiær, author (born 1863)
• 21 September – Edouard Suenson, business executive (born 1742)

October–December edit

• 8 October
  • Henning Frederik Feilberg, pastor, author and folklorist (born 1831)
  • Emma Eleonore Meyer, painter (born 1859)
• 27 November – Ole Sarvig, pet (died 1981)