- Jun 1 British submarine "Thetis" sinks in Liverpool Bay with all 99 aboard
- Jun 1 First night MLB game takes place at Philadelphia's Shribe Park; Phillies lose 5-2 to Pittsburgh Pirates
- Jun 1 Retired German Colonel-general Gerd von Runstedt returns to service
- Jun 3 "Beer Barrel Polka" by Will Glahe hits #1 on the pop singles chart
- Jun 3 71st Belmont: James Stout riding Johnstown wins in 2:29.6
- Jun 6 NY Giants beat Reds 17-3, with 5 HRs in 4th inning
- Jun 6 NY supreme court justice J F Crater legally declared dead
- Jun 6 The ship MS St. Louis, carrying 907 Jewish refugees from Europe, begins sailing back to the continent after it was refused entry into America. Approximately a quarter of those on board would perish in the Holocaust.
- Jun 10 MGM cartoon character Barney Bear debuts
- Jun 11 British ruler King George VI and Queen Elizabeth taste their first "hot dogs" at a party at FDR's Hyde Park residence during their US visit [1]
- Jun 12 Baseball Hall of Fame is dedicated in Cooperstown, New York
- Jun 12 Shooting begins on Paramount Pictures' Dr. Cyclops, the first horror film photographed in three-strip Technicolor.
43rd US Men's Open
Jun 12 US Open Men's Golf, Philadelphia Cricket Club: Byron Nelson wins by 3 strokes from Craig Wood and 7 ahead of Denny Shute in a 36-hole playoff to claim the second of his 5 major titles
- Jun 17 44th Women's French Championships: Simonne Mathieu beats Jadwiga Jedrzejowska (6-3, 8-6)
French Men's Championship
Jun 17 French Championships Men's Tennis: American collegiate champion Don McNeill beats countryman Bobby Riggs 7-5, 6-0, 6-3
- Jun 17 Last public guillotining in France. Eugen Weidmann, a convicted murderer, is guillotined in Versailles outside the prison Saint-Pierre
- Jun 20 Test flight of 1st rocket plane using liquid propellants
Lou Gehrig Retires
Jun 21 NY Yankees announce Lou Gehrig's retirement after doctors reveal he has amyotrophic lateral sclerosis
Elizabeth Meets Philip
Jun 22 Princess and future Queen Elizabeth meets future husband Prince Philip of Greece (Midshipman Mountbatten, RN)
Nagurski vs Thesz
Jun 23 Bronko Nagurski beats Lou Thesz in Houston, to win National Wrestling Association world heavyweight title
- Jun 23 France turns over Sanjak of Alexandretta (Hatay) to Turkey
- Jun 23 US Congress establishes US Coast Guard Reserve (renamed US Coast Guard Auxiliary 1941) as uniformed volunteer units supporting the Coast Guard
- Jun 24 Pan Am's 1st US to England flight
- Jun 27 1st night game at Cleveland Municipal Stadium (Indians 5, Tigers 0)
Headley Scores 107
Jun 27 Brilliant West Indies batsman George Headley scores 107 to follow his 106 in the 1st innings in 1st cricket Test v England at Lord's; England still wins by 8 wickets
- Jun 27 Brooklyn Dodgers tie Boston Bees, 2-2 in 23 innings; called on account of darkness after 5 hours 15 minutes
- Jun 28 Pan Am opens southern route transatlantic air service (Dixie Clipper)
- Jun 28 Yanks hit 13 HRs, sweep A's 23-2 & 10-0
- Jun 29 4th Dutch government of Prime Minister Hendrikus Colijn falls
- Jun 29 Dixie Clipper completes 1st commercial plane flight to Europe
Ford-Ferguson 9N Tractor
Jun 29 Ford introduces the revolutionary Ford-Ferguson 9N tractor incorporating Harry Ferguson's three-point hitch system
- Jun 30 Heinkel He 176 rocket plane flies for 1st time, at Peenemunde