Born in Milan, Malipiero was the son of cellist Riccardo Malipiero (1886–1975). He studied piano at the Milan Conservatory where he graduated in 1932. He then studied music composition at the Turin Conservatory where he obtained a diploma in 1937. He pursued further studies in composition with his uncle Gian Francesco Malipiero. From 1935 to 1947 he was a lecturer at the Liceo Musicale "Vincenzo Appiani". In 1979 he joined the music faculty at the Varese Conservatory where he taught for many years.