- Jun 1 California gets its 1st seismograph
- Jun 3 Baseball poem "Casey at the Bat" 1st published by the San Francisco Examiner
Event of Interest
Jun 5 US Democrats nominate Grover Cleveland for president

Grover Cleveland
Event of Interest
Jun 15 Wilhelm II becomes Emperor of Germany

Wilhelm II
- Jun 15 US National Championship Women's Tennis, Philadelphia Cricket Club: Bertha Townsend beats defending champion Ellen Hansell 6-3, 6-5
Presidential Convention
Jun 23 Frederick Douglass is 1st African-American to be nominated for US Vice President

Frederick Douglass
Presidential Convention
Jun 25 Republican Convention in Chicago nominates Benjamin Harrison

Benjamin Harrison
- Jun 29 First (known) recording of classical music made, Handel's Israel in Egypt on wax cylinder