- Jun 1 Simon Gallup, English bassist (The Cure)
- Jun 2 Tony Hadley, rock vocalist (Spandau Ballet-True)
- Jun 6 Steve Vai, American rock guitarist (Frank Zappa, David Lee Roth Band, Whitesnake), born in Carle Place, New York
- Jun 8 Mick Hucknall, English singer-songwriter (Simply Red), born in Manchester, England
- Jun 18 West Arkeen, American musician, best known for co-writing several Guns N' Roses songs (It's So Easy, The Garden), born in Neuilly-sur-Seine, France (d. 1997)
- Jun 19 Simon Wright, heavy metal drummer (AC/DC)
- Jun 19 Luke Morley, British rock guitarist (Thunder), born in Chamberwell, London
- Jun 20 John Taylor, English musician (Duran Duran), born in Solihull, Warwickshire
- Jun 23 Donald Harrison, American jazz saxophonist, born in New Orleans, Louisiana
- Jun 23 Tatsuya Uemura, Japanese arcade game musician and programmer, born in Japan
- Jun 25 Zorica Kondža, Croatian pop singer (Stijene), born in Split, Yugoslavia
- Jun 26 Zachary Breaux, American jazz guitarist, born in Port Arthur, Texas (d. 1997)
- Jun 29 "The Caveman" Kevin Shirley, South African music producer and mixer (Journey, Iron Maiden, Europe, Led Zeppelin), born in Johannesburg, South Africa
- Jun 30 Murray Cook, Australian children's singer (The Wiggles), born in Cowra, New South Wales, Australia
- Jun 30 Brenden O'Brien, American record producer (Pearl Jam; Stone Temple Pilots; Bruce Springsteen), born in Atlanta, Georgia
About June 1960
How Old? 60 years old
Generation: Baby Boomer
Leap Year: Yes