- Jun 1 Ferdinando Paer, composer
- Jun 3 Charles Bernard Desormes, French physicist and chemist who determined the ratio of the specific heats of gases and the composition of carbon monoxide and carbon disulfide, born in Dijon, France (d. 1862)
- Jun 3 Sydney Smith, English preacher, reformer and author, born in Woodford, Essex (d. 1845)
- Jun 5 Ernest Augustus I, Duke of Cumberland and King of Hanover (1837-51), born in Buckingham House, London (d. 1851)
- Jun 5 Willem Frederik van Bylandt, Dutch military officer, born in The Hague, Netherlands (d. 1855)
- Jun 12 Patrick Gass, sergeant of Lewis and Clark Expedition, born in Philadelphia, Pennsylvania (d. 1870)
- Jun 19 Joseph Diez Gergonne, French mathematician, born in Nancy, France (d. 1859)
- Jun 20 Thomas Douglas, 5th Earl of Selkirk, Scottish philanthropist, born in St Mary's Isle, Kirkcudbrightshire, Scotland (d. 1820)
- Jun 24 Éleuthère Irénée du Pont, French-American chemist and industrialist (E. I. du Pont de Nemours and Company), born in Paris (d. 1834)