Events in Sport
- Jun 1 Czech distance runner Emile Zatopek breaks his own 10,000m world record, clocking 28:54.2 in Brussels, Belgium
- Jun 12 86th Belmont: Eric Guerin aboard High Gun wins in 2:30.8
- Jun 12 Milwaukee Braves spot starting pitcher Jim Wilson throws first no-hitter in history of County Stadium when he blanks Philadelphia Phillies, 2-0
Boxing Title Fight
Jun 17 Rocky Marciano beats Ezzard Charles by unanimous points decision in his 3rd world heavyweight boxing title defence at Yankee Stadium, NYC

Rocky Marciano

Ezzard Charles
- Jun 19 US Open Men's Golf, Baltusrol GC: Ed Furgol wins his only major title, 1 stroke ahead of runner-up Gene Littler
Event of Interest
Jun 19 LPGA Western Open Women's Golf, Glen Flora CC: Betty Jameson wins 6 & 5 over Louise Suggs in the final

Louise Suggs
- Jun 26 Jim Peters runs marathon in 2:17:39.4
- Jun 27 Hungary beats Brazil, 4-2 in the "Battle of Berne" as FIFA World Cup quarter-final descends into an all-out brawl with 3 players sent-off; fighting continues in dressing rooms after final whistle
Birthdays in Sport
- Jun 3 Wally Weir, Quebec ice hockey player
- Jun 5 Phil Neale, English cricketer and coach, born in Scunthorpe
- Jun 7 Lui Passaglia, CFL place kicker (BC Lions), born in Vancouver, British Columbia
- Jun 11 Gary Fencik, American NFL defensive back (Chicago Bears), born in Chicago, Illinois
- Jun 11 John Dyson, Australian cricketer (NSW & Australian opening batsman), born in Kogarah, Sydney, Australia
- Jun 13 Daniel Seemiller, American table tennis player, born in Pittsburgh, Pennsylvania
- Jun 15 Beverley Whitfield, Australian swimmer (Olympic Gold 1972), born in Wollongong, Australia (d. 1996)
- Jun 20 Alan Lamb, South African/British cricket player (79 tests for England), born in Langebaanweg, Cape Province
- Jun 21 Jeremy Coney, New Zealand cricketer (NZ captain turned them into world-beaters), born in Wellington, New Zealand
- Jun 25 John C. Kimmel, American horse trainer, born in East Orange, New Jersey
- Jun 29 Rick Honeycutt, American baseball pitcher (St Louis Cardinals), born in Chattanooga, Tennessee