1759 in Denmark

• Monarch – Frederick V^[1]
• Prime minister – Johan Ludvig Holstein-Ledreborg

Undated

• Construction of Christian's Church, Copenhagen is completed.
• The settlement of Aasiaat is founded as Egedesminde in Greenland.
• The village of Havredal is founded.

• 15 January – Jørgen Mandix, judge (died 1835)^[2]
• 12 March – Rasmus Nyerup, literary historian, philologist, folklorist and librarian (died 1829)
• 5 April – Erik Viborg, veterinarian and botanist (died 1822)
• 14 July – Frederik Gottschalk von Haxthausen, Danish military officer and Norway's first minister of finance (died 1825)
• 19 July – Christopher Friedenreich Hage, merchant (died 1849)
• 11 December – Johan David Vogel, businessman and brewer (died 1728)

• 4 April – Christoffer Foltmar, painter and organist (born 1718)
• 9 May – Johan Friederich Wewer, merchant (born 1699)
• 5 September – Lauritz de Thurah, architect (born 1706)
• 10 September – Frederik Kaas, naval officer (born 1730)
• 6 October – Johann Gottfried Burman Becker, pharmacist, writer and illustrator (died 1860)
• 29 October – Anne Dorthe Lund, actress (date of birth unknown)