- Apr 1 Bruno Coquatrix, French music impresario (b. 1910)
- Apr 2 Carroll Rosenbloom, American businessman and NFL team owner (Baltimore Colts, LA Rams), dies of a heart attack at 72
- Apr 2 Ivan Barrow, Jamaican cricket wicketkeeper (11 Tests; first West Indian Test century-maker in England), dies at 68
- Apr 4 Edgar Buchanan, American actor (Petticoat Junction), dies at 76
- Apr 4 Zulfikar Ali Bhutto, Pakistani president, hanged in Pakistan at 51
- Apr 5 Eugène Gabritschevsky, Russian biologist and artist (b. 1893)
- Apr 6 M Marie Wadlow, American softball pitcher (Hall of Fame 1957), dies at 61
- Apr 6 Milton Ager, American composer, dies at 85
- Apr 7 Bruno Apitz, German writer, dies at 78
- Apr 9 Staats Cotsworth, American actor (Hamlet, Peyton Place), dies at 71
- Apr 10 Henriette P "Hetty" Beck, Dutch actress (Dodendans), dies at 91
- Apr 10 Nino Rota [Giovanni Rota Rinaldi], Italian classical and film score composer (Il cappello di paglia di Firenze; The Godfather (I & II; 16 Fellini films), dies from a coronary thrombosis at 67
- Apr 12 Pernell Charity, American blues guitarist, singer, and songwriter, dies at 58
- Apr 19 Rogers Morton, American politician (Member of the U.S. House of Representatives from Maryland), dies at 64
- Apr 20 Peter Donald, British-born American actor and radio host dubbed "one of radio's great dialecticians" (Masquerade Party), dies at 60
- Apr 23 Blair Peach, New Zealand-born anti-fascist (b. 1946)
- Apr 23 Doug Rauch, American rock and jazz-fusion bassist (Santana, 1972-74), dies of a heroin overdose at 28
- Apr 24 John Carroll [Julian LaFaye], American actor (Flying Tigers, Go West), dies from leukaemia at 72
- Apr 28 Feliks Roderyk Łabuński, Polish composer, dies at 86
- Apr 29 Julia Perry, American classical composer (Soul Symphony; Cask of Amontillado; Homunuclus C.F.) dies at 55
- Apr 29 Hardie Gramatky, American author and animator (Little Toot), dies at 72