• Monarch – Frederik IX^[1]
• Prime minister – Jens Otto Krag

• 21 March – Denmark hosts the Eurovision Song Contest and finishes in 9th place.
• 22 September – The 1964 parliamentary election is held.

• January–February – Denmark participates in the 1964 Winter Olympics.
• October – Denmark participates in the 1964 Summer Olympics and wins six medals.

Badminton edit

• 1–4 April – All England Open Badminton Championships
  • Knud Aage Nielsen wins gold in Men's Single
  • Finn Kobberø and Jørgen Hammergaard Hansen win gold in Men's Double
  • Karin Jørgensen and Ulla Strand win gold in Women's Double

Football edit

• 19 April – Naja Abelsen, painter and illustrator
• 30 March – the 1964 Jutland Series is launched
• 7 May – Esbjerg fB wins the 1963–64 Danish Cup by defeating KFUMs Boldklub Odense 2–1 in the final.
• 17–20 June – Denmark participates in 1964 European Nations' Cup in France.
  • 17 June – Denmark is defeated by the Soviet Union in the semi-final.
  • 20 June – Denmark is defeated by Hungary in the bronze match.
• 15 November – the 1964 Jutland Series final is played

January–March edit

• 13 January – Claus Nielsen, footballer
• 4 February – Marianne Gaarden, bishop
• 21 March – Jesper Skibby, cyclist

April–June edit

• 3 April – Bjarne Riis, cyclist
• 8 April – Janne Teller, author
• 6 May – Lars Mikkelsen, actor
• 15 May – Lars Løkke Rasmussen, 25th Prime Minister of Denmark
• 1 June – Marianne Florman, handball player
• 15 June – Michael Laudrup, football player
• 30 June – Alexandra, Countess of Frederiksborg, Ex-wife of Prince Joachim of Denmark

July–September edit

• 6 August Sara Blædel, author

• 9 September – Cæcilie Norby, jazz and rock singer
• 18 September – Curt Hansen, chess grandmaster
• 25 September – Ida Jessen, author

October–December edit

• 11 October – Christian Dyrvig, businessman
• 3 November – Paprika Steen, actress
• 20 December – Morten Løkkegaard, politician

January–March edit

• 1 January – Thyge Petersen, boxer (born 1902)

January–March edit

• 16 February – Jette Bang photographer (born 1914)
• 27 March – Emil Reesen, composer, conductor and pianist (born 1887)

April–June edit

• 10 May – Harald Tandrup, writer (born 1874)
• 5 June – Lauge Koch, geologist and Arctic explorer (born 1892)
• 21 May – Sigurd Kielland Brandt, painter (born 1886)

July–September edit

• 14 July – Prince Axel of Denmark (born 1888)
• 12 August – Jørgen Skafte Rasmussen, businessman, company founder (born 1878)
• 28 September – Arild Rosenkrantz, nobleman, painter, sculptor, stained-glass artist and illustrator (born 1870)

October–December edit

• 21 October – Carl Johan Hviid, actor (born 1899)
• 26 November – Bodil Ipsen, actress and film director (born 1889)

• 1964 in Danish television