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

• 6 January – the Faroese Society is formed.
• 26 February – Akademisk Boldklub is founded.
• 9 May – the Edouard Suenson Memorial is inaugurated on Store Kongensgade.
• 18 May – the Danish Football Association is established.

Undated

• Langelandsgade Kaserne is completed and opens as a military barracks.
• Kvindevalgretsforeningen is established by Line Luplau to promote women's suffrage.
• The company Dampskibsselskabet Torm is established by Ditlev Torm and Christian Schmiegelow in Copenhagen.

January–March edit

• 11 January – Niels Peter Holbech, painter (died 1804)
• 3 February – Carl Theodor Dreyer, film director (died 1968)

April–June edit

• 16 May – Maria Garland, actor (died 1967)
• 29 May – Aksel Agerby, composer, organist, and music administrator (died 1942)
• 30 May – Anker Engelund, engineer and university professor (died 1861)

July–September edit

• 30 August – Bodil Ipsen, actress (died 1964)
• 4 September – Aage Rasmussen, photographer and track and field athlete (died 1983)

October–December edit

• 13 October – Margrete Drejer, textile artist (died 1975)
• 17 November – Axel Saltom ceramist (died 1961)
• 21 November – Niels Larsen, sport shooter (died 1969)

• 9 May – William Hammer, painter (born 1821)
• 2 May – Edward Tesdorpf, landowner (born 1817)
• 17 July – Auguste Sophie Friederike, princess of Hesse-Kassel (born 1823)
• 28 November – Erling Eckersberg, engraver (born 1808)