• Monarch – Christian VII^[1]
• Prime minister – Ove Høegh-Guldberg

• 1 May – The Royal Danish Porcelain Factory is founded by the chemist Frantz Heinrich Müller, who is given a 50-year monopoly to create porcelain in Denmark, and begins operations in a converted post office.

Undated edit

• Bygholm Manor is completed near Horsens.^[2]
• Vincenzo Galeotti succeeds Vincenzo Piatolli as artistic director of the Royal Danish Ballet.
• Nicolai Abildgaard completes The Wounded Philoctetes.

• 16 March – Martin Lehmann, engraver (died 1856)
• 27 March – Nicolai Abraham Holten, banker and civil servant (died 1850)
• 22 June – Ulrich Anton Schønheyder, naval officer (died 1858)
• 2 July – Joachim Melchior Magens, colonial administrator and lawyer (died 1845)
• 12 August – Conrad Malte-Brunm, geographer and journalist (died 1826)
• 17 September – Margrethe Schall, dancer (died 1852)
• 9 October – Peter Thonning, physician and botanist (died 1848)
• 19 October – Kamma Rahbek, salonist and lady of letters (died 1829)
• 1 November – Christian Adolph Diriks, lawyer (died 1837)
• 8 November – Jacob Peter Mynster, theologian and bishop (died 1854)

• 30 March – Christian Ditlev Reventlow, Privy Councillor and nobleman (born 1710)
• 10 April – Jonas Haas, engraver (born 1720)
• 15 June – Joost van Hemert, merchant and ship-owner (born 1696)
• 16 August – Jakob Langebek, historian (born 1710)
• 16 October – Peter van Hurk, businessman (born 1697)
• 25 November – Jacob Benzon, nobleman, civil servant and Governor-general of Norway (born 1688)