- Jun 1 Napoleon Eugene, the last dynastic Bonaparte, is killed serving with British forces in the Anglo-Zulu War. He is buried in Farnborough, Hampshire.
- Jun 5 13th Belmont: George Evans riding Spendthrift wins in 2:42.75
- Jun 16 Gilbert & Sullivan's "HMS Pinafore" debuts at Bowery Theater NYC
- Jun 18 W. H. Richardson, an African-American inventor, patents the children's carriage (Patent no. 405599)
- Jun 21 Frank W. Woolworth opens his 1st successful "F. W. Woolworth Great Five Cent Store" on North Queen Street, Lancaster, Pennsylvania
- Jun 21 Infielder William White plays one game for the Providence Grays with conjecture was the first African-American to play MLB even though he appeared Caucasian
- Jun 26 Ismael Pasha resigns as khedive of Egypt
- Jun 30 Ex-khedive Ismael Pasha leaves Cairo with train full of stolen goods