Francesco Gonzaga (1444 - 21 October 1483) was an Italian bishop and cardinal.
Born at Mantua, he was the second son of Ludovico II Gonzaga, marquess of Mantua, and Barbara of Brandenburg.
He was appointed as cardinal by Pope Pius II aged seventeen, just after the Council of Mantua. He received the title of Santa Maria Nuova.
He became bishop of Brixen in 1466 and bishop of Mantua two years later. In 1476 he was appointed as bishop of Bologna. In 1477 he had an illegitimate son, Francesco, who died in 1511. In 1479-1480 he housed in his court at Mantua Angelo Poliziano, who wrote there the Fabula of Orpheus. Like other members of the family, he collected ancient findings and gems.
He died at Porretta Terme in 1483.