Events in Sport
- Jun 1 The Riverside International Raceway in Southern California opens with three 500-mile races in one weekend; Eddie Gray wins the Crown America 500 for NASCAR Grand National cars
- Jun 2 Brooks Robinson hits into 1st of record 4 triple plays
Baseball Record
Jun 2 Yankees pitcher Whitey Ford fans 6 in a row to tie an AL record

Whitey Ford
LPGA Championship
Jun 8 LPGA Championship, Churchill Valley CC: Mickey Wright wins first of 13 major titles by 6 strokes from Fay Crocker

Mickey Wright
US Golf Open
Jun 14 US Open Men's Golf, Southern Hills CC: Native Oklahoman Tommy Bolt wins his only major championship, 4 strokes ahead of 22-year old South African Gary Player

Gary Player
- Jun 22 Game in KC between A's & Red Sox delayed 29 minutes due to tornado
- Jun 22 LPGA Western Open Women's Golf, Kahkwa CC: Patty Berg wins back-to-back WO titles; beats runner-up Beverly Hanson by 4 strokes
- Jun 28 American swimmer Nancy Ramey sets world record for 100m butterfly in 1:09.6 in Los Angeles, California
- Jun 28 US Open Women's Golf, Forest Lake CC: Mickey Wright wins 1st of 4 Open titles by 5 from Louise Suggs; 1st player to win Open & LPGA in same year
FIFA World Cup
Jun 29 FIFA World Cup Final, Råsunda Stadium, Stockholm, Sweden: Vavá & Pelé each score 2 goals as Brazil beats Sweden, 5-2

Pele
Birthdays in Sport
- Jun 4 Tony Pigott, English cricketer (England pace bowler in a Test v NZ 1984), born in Fulham, London, England
- Jun 7 Philippe Boccara, American kayaker (Olympics silver 1996; World C'ship gold 1985, 87, 90-91), born in Le Mans, France
- Jun 14 Eric Heiden, American speed skater (5 Olympic gold medals 1980), born in Madison, Wisconsin
- Jun 15 Wade Boggs, American Red Sox/Yank 3rd baseman (AL bat champ 1985-88), born in Omaha, Nebraska
- Jun 16 Ulrike Tauber, East German swimmer
- Jun 20 Dickie Thon, baseball player
- Jun 20 Ron Hornaday, American racecar driver
- Jun 24 T. C. Chen, Taiwanese golfer (US Open 1985 runner-up), born in Taipei City, Taiwan
- Jun 25 Debbie Green-Vargas, American volleyball player (Olympic silver 1984), born in South Korea
- Jun 28 Sergei Shakrai, Russian figure skater (Olympic silver 1980), born in Soviet Union
- Jun 29 Rosa Mota, Portuguese long distance runner (Olympic gold marathon 1988; World C'ship gold marathon 1987), born in Porto, Portugal
Weddings in Sport
Wedding of Interest
Jun 22 NBA forward Elgin Baylor (23) weds Ruby Saunder at Mt Olive Baptist Church in Washington, D.C.

Elgin Baylor
Deaths in Sport
- Jun 7 Roger Hartigan, cricketer (2 Tests for Aust in 1908), dies
Clarence DeMar
Jun 11 Clarence DeMar [Mr. DeMarathon], American marathon runner and 7-time winner of the Boston Marathon, dies of cancer at 70

Clarence DeMar