On 9 July 1657, Enríquez de Rivera was appointed the Bishop of Guatemala in the Viceroyalty of New Spain by Pope Alexander VII.

In Guatemala he ordained the first Bethlehemites, a religious order recently founded in that colony by St. Peter of Saint Joseph Betancur, to advance to the priesthood, and he began the construction of the Hospital de San Pedro.

In January 1668 Enríquez de Rivera was transferred by Pope Clement IX to the Diocese of Michoacán in New Spain, but while he was on the road to take up his new position, news reached him that he was to become, instead, the Archbishop of Mexico.

On that day, the Inquisitor, Juan de Ortega, delivered the sealed instructions to the Audiencia, and the government was transferred to the archbishop.

Among Enríquez de Rivera's acts as viceroy were many public works projects, not only in Mexico City but also in outlying areas.

[1] In 1667 the viceroy founded the village of Paso del Norte (now Ciudad Juárez), on the Río Bravo and the road to Albuquerque.

He retired to the rural Monastery of Nuestra Señora del Risco in the Sierra de Ávila, where he died in 1684.