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

• 2 January – FLSmidth, a supplier of cement production technology, is founded by Frederik Læssøe Smidth as a small "technical bureau" based in a single room of his mother's apartment.^[2]
• 10 June – Hjedding Dairy is established as Denmark's first cooperative dairy.
• 5 November – Carl Jacobsen's sculpture collection, which later forms the basis of the Ny Carlsberg Glyptotek, is opened to the public in his winter garden.^{[citation needed]}

Undated edit

• A group of dissatisfied students from the Royal Danish Academy of Fine Arts founds the Artists' Studio School as a reaction to the outdated teachings at the Academy.

January–March edit

• 11 February – Knud V. Engelhardt, industrial designer (died 1931)

April–June edit

• 5 April – Karen Callisen, geologist (died 1970)
• 25 April – Christian Mortensen, world's oldest man of his day (died 1998)
• 2 May – Sophus Black, telegraph manager and art collector (d. 1960)
• 7 May – Thorvald Niss, painter (died 1905)

July–September edit

• 19 September – Robert Storm Petersen, cartoonist, painter, humorist, writer (died 1949)

October–December edit

• 16 November – Kai Nielsen, sculptor (died 1924)

• 28 January – Hans Jørgen Hammer, painter (born 1815)
• 24 August – Niels Christian Kierkegaard, craftsman and lithographer (nprm 1906)
• 24 October – Margit Brandt, fashion designer (born 1945)
• 4 December – Wilhelm Wanscher, businessman and art collector (born 1802)