• Monarch – Christian IX^[1]
• Prime minister – C. E. Frijs

• 22 August – SS Ottawa departs from Copenhagen as the first emigration ship between Copenhagen and New York City.
• 7 September – The engagement of Princess Dagmar and Grand Duke Alexander Alexandrovich is celebrated at the royal court at Christiansborg Palace.^[2]
• 22 September – Princess Dagmar leaves Copenhagen on board the steam ship Slesvig.^[2]

January–March edit

• 1 January – Peter Elfelt, photographer (died 1931)
• 19 January – Carl Theodor Zahle, politician (died 1946)
• 16 February – Charles Brun, politician (died 1919)
• 25 February – Hans Peter Prior, industrialist (died 1936)

April–June edit

• 5 May – Thomas B. Thrige, industrialist (died 1938)
• 19 June – Sabine Helms, botanist (died 1929)

July–September edit

• 3 July – Albert Gottschalk, painter (died 1906)
• 15 July – Adolph Jensen, economist and statistician (died 1948)
• 31 August – Georg Jensen, goldsmith, designer (died 1935)

October–December edit

• 9 November – Georg Carl Amdrup, admiral, polar explorer (died 1947)
• 6 October – Nina Bang, politician (died 1928)
• 2 December – Holger Nielsenm fencer (died 1955)

• 16 December – Christian Albrecht Bluhme, politician, prime minister of Denmark (born 1794)