Events in Sport
- Jun 3 European Cup Final, Stuttgart: Real Madrid beats Stade de Reims, 2-0; 4th consecutive title for Los Blancos
US Golf Open
Jun 11 Charlie Sifford becomes the 1st African American to play in a US Golf Open
Charlie Sifford
- Jun 12 SF Giants Mike McCormick no-hits Phillies, 3-0 in 5 inning game
- Jun 13 91st Belmont: Bill Shoemaker aboard Sword Dancer wins in 2:28.6
- Jun 14 US Open Men's Golf, Winged Foot GC: Billy Casper wins first of his 2 Open titles, 1 stroke ahead of runner-up Bob Rosburg
- Jun 22 Most Phillies strike out in a game (16 by Sandy Koufax)
Boxing Title Fight
Jun 26 Ingemar Johansson TKOs Floyd Patterson in 3 for heavyweight boxing title
Floyd Patterson
US Women's Golf Open
Jun 27 US Open Women's Golf, Churchill Valley CC: Mickey Wright successfully defends her Open title by 2 strokes from Louise Suggs
Mickey Wright
Louise Suggs
- Jun 28 Phils Wally Post is only outfielder to throw out 2 runners in an inning twice (Losing to Giants 6-0)
Birthdays in Sport
- Jun 1 Martin Brundle, British race car driver and F1 television commentator
- Jun 2 Charlie Huddy, Oshawa, NHL defenseman (Buffalo Sabres)
- Jun 3 Sam Mills, NFL linebacker (New Orleans Saints and Carolina Panthers), (d. 2005)
- Jun 4 Rod Connop, Canadian CFL corner (Edmonton Eskimos), born in North Vancouver, British Columbia
- Jun 6 David Schultz, American wrestler (d. 1996)
- Jun 12 Jalal-ud-din, Pakistani cricketer (Pakistani paceman, ODI hat-trick v Aust 1982), born in Karachi, Pakistan
- Jun 12 Steve Bauer, Canadian road racer cyclist (Olympic silver 84, 96), born in St. Catharines, Canada
- Jun 21 Tom Chambers, NBA forward, center (Seattle SuperSonics, Phoenix Suns)
- Jun 24 Rob Delahaye, soccer player (MVV)
- Jun 25 Jari Puikkonen, Finnish ski jumper (Winter Olympics medalist), born in Lahti, Finland
- Jun 30 Michel Dion, Canadian Rifle shooter (Olympics 24-92, 96), born in Quebec City, Québec