Events from the year 1735 in Denmark.

• Monarch – Christian VI^[1]
• Prime minister – Iver Rosenkrantz (until 12 May), Johan Ludvig Holstein-Ledreborg

• Vemmetofte Convent is established after the death of Princess Sophia Hedwig through her will.

• 6 January – Otto Christopher von Munthe af Morgenstierne, civil servant, judge and landowner (died 1809)
• 1 March – Caroline Thielo, actress (died 1754)
• 4 May – Jacob Baden, philologist and critic (died 1904)
• 23 June – Johan Boye Junge, master carpenter, developer and director of Copenhagen Fire Corps (died 1807)
• 28 August – Andreas Peter Bernstorff, politician (died 1797)

• 13 March – Princess Sophia Hedwig, princess of Denmark (born 1677)
• 22 April - Lorentz Reichwein, military officer (born 1680)