- Jun 3 93rd Belmont: Braulio Baeza aboard Sherluck wins in 2:29.2
Event of Interest
Jun 4 LPGA Western Open Women's Golf, Belle Meade CC: Mary Lena Faulk wins by 6 strokes ahead of runner-up Betsy Rawls

Betsy Rawls
- Jun 8 Test Cricket debut of William Morris Lawry, v England at Edgbaston, 57
Baseball Record
Jun 8 Milwaukee sets record of 4 consecutive HRs (Eddie Mathews, Hank Aaron, Joe Adcock & Frank Thomas)

Hank Aaron
- Jun 9 Ryne Duren sets AL record with 7 straight strikeouts against Red Sox
Baseball Record
Jun 11 Roger Maris hits 19th & 20th of 61 HRs

Roger Maris
- Jun 17 US Open Men's Golf, Oakland Hills CC: Gene Littler wins his sole major title, 1 stroke ahead of runners-up Bob Goalby and Doug Sanders
- Jun 19 NY Yankee Roger Maris hits his 25th of 61 HRs
Event of Interest
Jun 23 Cubs Ernie Banks ends his 717 consecutive-games-played streak

Ernie Banks
Baseball Record
Jun 29 SF outfielder Willie Mays becomes the 4th player in MLB history with 3 or more home runs twice in one season with a 10th inning blast in Giants 8-7 win over the Phillies in Philadelphia

Willie Mays