- Jun 1 French Championships Men's Tennis: Sven Davidson becomes first Swede to win a Grand Slam title; beats American Herbert Flam 6-3, 6-4, 6-4
- Jun 1 French Championships Women's Tennis: England's Shirley Bloomer wins her lone Grand Slam singles title; beats American Dorothy Knode 6-1, 6-3
Cricket History
Jun 4 England cricket batsmen Peter May (285no) & Colin Cowdrey (154) make 411 stand in drawn 1st Test v West Indies in Birmingham; WI spinner Sonny Ramadhin bowls mammoth 98 overs
LPGA Championship
Jun 10 LPGA Championship, Churchill Valley CC: Louise Suggs wins her 10th major tile by 3 strokes from Wiffi Smith
Baseball Record
Jun 12 Stan Musial plays in 823rd game (new NL consecutive-game streak)
Baseball Record
Jun 13 Ted Williams becomes 1st ALer to have 2, 3-HR games in a season
Belmont Stakes
Jun 15 89th Belmont: Bill Shoemaker aboard Gallant Man wins in 2:26.6
US Golf Open
Jun 15 US Open Men's Golf, Inverness Club: Dick Mayer defeats defending champion Cary Middlecoff by 7 strokes in an 18-hole playoff to win his only major title
Baseball Trade
Jun 15 Yanks trade Billy Martin & Ralph Terry for Ryne Duran
- Jun 16 White Sox reliever Dixie Howell hits 2 HRs to beat Washington Senators 8-6
- Jun 25 2nd Rugby League World Cup: New Zealand beats Great Britain 29-21
- Jun 28 Frick overrules and names Stan Musial, Willie Mays, & Hank Aaron to team
US Women's Golf Open
Jun 29 US Open Women's Golf, Winged Foot GC: Betsy Rawls wins when apparent champion, Jackie Pung at 298 (+6) is disqualified for signing an incorrect scorecard kept by playing partner Betty Jameson