- Jun 1 Texas constitutional convention meets in Austin
- Jun 1 Treaty of Bosque Redondo is signed allowing the Navajos to return to their lands in Arizona and New Mexico
- Jun 4 Van Bosse/Fock government begins
- Jun 9 1st meeting of Board of Regents, University of California
- Jun 10 2nd Belmont: Bobby Swim aboard General Duke wins in 3:02
- Jun 13 Oscar Dunn becomes first African American to be elected a Lieutenant Governor, of Louisiana
- Jun 19 Major general E R S Canby removes mayor of Columbia, South Carolina
- Jun 21 Wagner's opera "Meistersinger von Nuernberg" premieres in Munich
- Jun 22 Arkansas re-joins the US
- Jun 23 Christopher Latham Sholes patents the typewriter with a QWERTY keyboard
- Jun 25 Florida, Alabama, Louisiana, Georgia, North Carolina and South Carolina readmitted to US
- Jun 25 US President Andrew Johnson passes a law that government workers would work 8 hr day