• Monarch – Margrethe II^[1]
• Prime minister – Anker Jørgensen

• 8 December – The 1981 Danish parliamentary election is held.

Badminton edit

• Gentofte BK wins Europe Cup.

Cycling edit

• Albert Fritz (FRG) and Patrick Sercu (BEL) win the Six Days of Copenhagen six-day track cycling race.

January–March edit

• 9 February – Kristian Pless, tennis player
• 5 March – Helle Frederiksen, triathlete

April–June edit

• 30 May – Lars Møller Madsen, handball player
• 9 June – Kasper Søndergaard, handball player

July–September edit

• 1 August – Hans Lindberg, handball player
• 1 September – Michael Maze, table tennis player
• 6 September – Søren Larsen, footballer

October–December edit

• 6 October – Thomas Troelsen, music producer
• 28 October – Elvira Lind, film director
• 24 November – Mads Rasmussen, rower
• 4 December – Brian Vandborg, cyclist

• 17 February – Ellen Gottschalch, actress (born 1894)
• 27 March – Preben Kaas (born 1930)
• 21 November – Ejner Federspiel, actor (born 1896)
• 28 November – Arthur Jensen, actor (born 1897)

• 1981 in Danish television