Francesco Gonzaga (6 December 1538 – 6 January 1566) was an Italian nobleman, who was Duke of Ariano.
He was brother of the Cardinal Gianvincenzo Gonzaga, nephew of Cardinal Ercole Gonzaga and of Francesco III Gonzaga, Duke of Mantua.
He was born in Palermo where his father Ferrante Gonzaga, count of Guastalla, was Viceroy. When Ferrante died in 1557 Ercole Gonzaga became guardian and the young Mantuan humanist and future Jesuit Antonio Possevino became tutor to the brothers. Francesco Gonzaga a member of the Academy of the Vatican Nights. As protonotary apostolic he obtained from Pius IV the Abbey of Acqua Nera, and on 26 February 1562 was created Cardinal of San Nicola in Carcere.
Francesco Gonzaga appointed as bishop of Mantua in 1565. He died in Rome the following year.
He also had down Syndrome.