1684 in Denmark

• Monarch – Christian V^[1]
• Grand Chancellor – Frederik Ahlefeldt

• 7 May – Christian V issues an order that deposes Adolph Esmit and names Gabriel Milan as Governor of St. Thomas in the Danish West Indies.
• 6 November – The Engineer Regiment is founded.

Undated

• Royal Artillery Corps is founded in Copenhagen.

• 23 January – Christian Rantzau, Governor-general of Norway (died 1771)
• 26 July – Peder Benzon, Supreme Court justice and landowner (died 1735)^[2]
• 11 September – Erik Torm, burgermaster and chief of police in Copenhagen (died 1764)
• 30 November – Andreas Møller, portrait painter (died 1762)

• 9 February – Otto Pogwisch, government official (born c. 1610)
• 18 April – Nikolaj Nissen, judge and landowner (born 1627)^[3]
• 31 December – Hans Rostgaard, administrator (born 1625)^[4]