- Apr 1 Nescafé introduces their flagship brand in Switzerland
5th Augusta National Invitation
Apr 4 5th Augusta National INvitation (Masters): Henry Picard wins his only Masters, 2 strokes ahead of runners-up Harry Cooper and Ralph Guldahl
Piston's 1st Symphony
Apr 8 Walter Piston's 1st Symphony in E, premieres in Boston, by the Boston Symphony, conducted by the composer
- Apr 10 Austria becomes a state of Germany
- Apr 10 NY makes syphilis test mandatory in order to get a marriage license
Government of Édouard Daladier
Apr 10 Second government of Blum replaced by Édouard Daladier's government in France
- Apr 12 1st US law requiring medical tests for marriage licenses (New York)
- Apr 12 Stanley Cup Final, Chicago Stadium, Chicago, IL: Chicago Black Hawks beat Toronto Maple Leafs, 4-1 for a 3-1 series win; only team to win Cup with losing regular season record
- Apr 13 Clifford Goldsmith's play "What a Life" premieres at The Biltmore Theater, NYC
- Apr 15 Anti-Jewish riots break out in in Dąbrowa Tarnowska, Poland
- Apr 16 Great Britain recognizes Italian annexation of Abyssinia
- Apr 18 42nd Boston Marathon won by Leslie Pawson in 2:35:34.8; his second victory in the event
- Apr 18 Headless Mad Butcher victim found in Cleveland
- Apr 19 Baker Bowl, Philadelphia: Phillies infielder Emmett "Heine" Mueller & Brooklyn Dodger outfielder Ernie Koy both homer in their 1st MLB at bats
- Apr 26 Austrian Jews required to register property above 5,000 Reichsmarks
- Apr 30 The first televised FA Cup Final takes place between Huddersfield Town and Preston North End