- Jun 1 Bell Phone opens 1st Dutch telephone exchange
- Jun 1 Ridden by outstanding English jockey Fred Archer, Iroquois wins the Epsom Derby to become first American-owned and bred horse to take out a European classic race
- Jun 2 Haarlem-Zandvoort Railway opens
- Jun 7 15th Belmont: T. Costello aboard Saunterer wins in 2:47
- Jun 12 The USS Jeannette, under the command of George Washington De Long, is crushed by Arctic ice after 21 months of ice-bound drifting
- Jun 13 The USS Jeannette, under the command of George Washington De Long, sinks in the Arctic circle following 21 months of drifting after becoming trapped in the ice
- Jun 14 Player piano patented by John McTammany Jr (Cambridge, Massachusetts)
- Jun 16 Austria-Hungary and Serbia sign military treaty
- Jun 19 Muhammad Ahmad becomes Mahdi of Sudan
- Jun 24 200 drown as train runs off bridge near Cuautla, Mexico
- Jun 30 Henry Highland Garnet named US minister to Liberia
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