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

Badminton edit

• 19–23 March – All England Badminton Championships
  • Erland Kops wins gold in Men's Singles
  • Finn Kobberø and Jørgen Hammergaard Hansen win gold in Men's Doubles
  • Finn Kobberø and Ulla Strand win gold medal in Mixed Doubles

Football edit

• 18 December – Denmark qualifies for the final tournament of the 1964 European Nations' Cup in France by defeating Luxemburg in the second round of the 1964 European Nations' Cup qualifying.

January–March edit

• 26 February – Jan Friis-Mikkelsen, chef and restaurateur
• 28 March – Morten Kirkskov, actor, theatre director and writer

April–June edit

• 7 April – Fredrik Lundin, jazz saxophonist
• 24 June – Jascha Richter, singer-songwriter, frontman of Michael Learns to Rock

July–September edit

• 4 July – Jan Mølby, football player, football coach
• 15 July – Brigitte Nielsen, actress, model, and singer
• 25 September – Peter Have, politician

October–December edit

• 3 October – Niels Lan Doky, jazz pianist, record producer
• 13 October – Henrik Qvortrup, journalist
• 18 November – Peter Schmeichel, footballer
• 6 December – Ulrich Thomsen, Danish actor and producer
• 26 December – Lars Ulrich, drummer, co-founder of Metallica
• 27 December – Claus Meyer, restaurateur, culinary entrepreneur, cookbook writer

• 20 February – Jacob Gade, violinist and composer (born 1879)
• 14 April – Anna Borg, Danish-Icelandic actress (born 1903)^[2]
• 3 July – Povl Baumann, architect (born 1878)
• 5 July – Aagot Lading, educator (died 1909)

• 1963 in Danish television