Federico Gonzaga (1540–February 21, 1565) (called the Cardinal of Monferrato) was an Italian Roman Catholic cardinal and bishop.
A member of the House of Gonzaga, Federico Gonzaga was born in Mantua in 1540. He was the posthumous son of Federico II Gonzaga, Duke of Mantua. His mother was Margaret Paleologa. He was the nephew of Cardinal Ercole Gonzaga. He was educated at the University of Bologna.
Pope Pius IV made him a cardinal priest in the consistory of January 6, 1563. He received the red hat and the titular church of Santa Maria Nova (a deaconry raised pro illa vice to the status of title) on March 4, 1563.
On June 4, 1563, he became administrator of the Diocese of Mantua, with dispensation for not having reached the canonical age. He was the papal legate in Mantua in 1564. He was granted the title of Bishop of Mantua on October 16, 1564, but never received consecration as a bishop.
He died in Mantua on February 21, 1565. He was buried in Mantua Cathedral.