Gaspar de Zúñiga Acevedo y Fonseca, 5th Count of Monterrey (1560 – March 16, 1606) was a Spanish nobleman who was the ninth viceroy of New Spain.

De Zúñiga y Acevedo also took part in the defense of the port of A Coruña when it was attacked by the English corsair Francis Drake in 1589.

In 1596, the viceroy Count of Monterrey reported, in a letter sent to Philip II to justify the increase of the salary of the royal officials, that those had seized and burned some delinquents for the unspeakable sin of sodomy, although he does not give the number of victims or the circumstances of the event.

In 1601, the Indians of Topia rose against the Spanish, but through the influence of Idefonso de la Mota, bishop of Guadalajara, they were pacified.

Oñate official search did not locate the legendary Seven Cities of Gold believed to be within the provinces of Cíbola and Quivira.

On this expedition Vizcaíno founded La Paz, Baja California Sur, so named because of his friendly reception there by the Indians.

Subsequent plans to colonize Alta California foundered when Zúñiga's successor, Juan de Mendoza, 3rd Marquis of Montesclaros, turned out to be much less favorable.

Here de Zúñiga y Acevedo hosted a week-long welcoming festival said to have cost more than a year's viceregal salary.

The new viceroy took over the administration of New Spain in October, and in that month de Zúñiga y Acevedo sailed from Acapulco for Lima.