- Jun 3 "Wildcat" closes at Alvin Theater NYC after 172 performances
- Jun 13 Billy Barnes' musical revue "Billy Barnes People", starting Ken Berry, Dave Ketchum, and Jo Anne Worley, opens at Royale Theater, NYC; runs for 7 performances
- Jun 16 Soviet ballet dancer Rudolf Nureyev defects to West at Le Bourget Airport in Paris, France
- Jun 17 Billy Barnes' musical revue "Billy Barnes People", starting Ken Berry, Dave Ketchum, and Jo Anne Worley, closes at Royale Theater, NYC, after 7 performances
- Jun 19 "Little Egypt (Ying-Yang)" by The Coasters peaks at #23
- Jun 22 Beatles record "Ain't She Sweet", "Cry for a Shadow", "When the Saints Go Marching In", "Why", "Nobody's Child" & "My Bonnie", in Hamburg, Germany
My Bonnie
Jun 22 Tony Sheridan & the Beatles record "My Bonnie" & "The Saints", produced by Bert Kaempfert, in Hamburg, Germany
- Jun 24 Jacques Offenbach and Yip Harburg's musical "The Happiest Girl in the World", starring Cyril Ritchard and Justine Rule, closes at Martin Beck NYC after 97 performances
- Jun 24 Tony Sheridan, backed by the Beatles, records "If You Love Me Baby" (aka "Take Out Some Insurance On Me, Baby") in Hamburg, Germany