• Monarch – Christian IX^[1]
• Prime minister – J. B. S. Estrup

• 24 May – the May 1881 Danish Folketing election is held.
• 26 July – the July 1881 Danish Folketing election is held.
• 1 October – the Herning–Skjern portion of the Skanderborg–Skjern line opens.
• 1 September – Rysensteen Gymnasium is established in Copenhagen.
• 21 September – the Statue of Niels Juel, created by the sculptor Theobald Stein, is unveiled in 1881 at Holmens Kanal.

Undated

• The Neye luggage company is established in Copenhagen.
• Danish Distillers open in Aalborg.

• 6 July – Nancy Dalberg, composer (died 1949)
• 11 September – Asta Nielsen, actress (died 1972)
• 6 October – Vilhelm Buhl, politician (died 1954)

• 9 March – Caroline Amalie of Augustenburg, Queen of Denmark (born 1796)
• 31 March – Princess Caroline of Denmark (born 1793)
• 21 June – Emil Normann, painter (born 1798)
• 20 September – Martin Hammerich, literary historian and educator (Born 1811)
• 24 September – Petrine Fredstrup, ballet dancer (born 1827)