- Jun 4 4th Belmont: W Dick aboard Kingfisher wins in 2:59.5
- Jun 5 Constantinople fire; 900 die
- Jun 9 Washington: Presdent Grant meets with Sioux chief Red Cloud
- Jun 11 1st-stone Amstel Brewery opens in Amsterdam
- Jun 14 All-pro Cincinnati Red Stockings suffer 1st loss in 130 games
- Jun 22 US Congress creates Department of Justice
- Jun 25 Opera "Die Walküre (The Valkyrie)" is produced (Munich)
- Jun 26 1st section of Atlantic City (NJ) Boardwalk opens
- Jun 26 Wagner's opera "Valkyrie" premieres in Munich
- Jun 28 U.S. Congress creates federal holidays (New Years Day, Independence Day, Thanksgiving Day, and Christmas Day), initially applicable only to federal employees
- Jun 30 Ada Kepley becomes 1st American female law college graduate (Old University of Chicago, later Northwestern)