Malevezzi was born in Lucca. From 1551 he lived in Florence, serving the Medicis from 1562. He held a number of organist posts in the city, and also taught pupils, among them Jacopo Peri, often regarded as the inventor of opera. Among his works are three books of madrigalss.
Malvezzi's brother Alberigo (around 1550-1615) was also an organist and composer.