In a letter to the faithful, Los Angeles Archbishop Jose Gomez said Zavala had told him in December that he had two children who lived with their mother in a different state. Zavala subsequently submitted his resignation to the pope.
The archdiocese has offered spiritual and financial aid to help the children with college costs, Gomez said in the letter posted on the blog of the Catholic News Service of the U.S. Conference of Catholic Bishops.
Roman Catholic priests are required to be celibate, though Eastern rite priests can be married and married Anglican priests who convert can become Catholic priests. The celibacy requirement is often blamed for discouraging many men who would otherwise consider the priesthood.
Also Wednesday, Pope Benedict XVI named Monsignor Cirilio Flores to eventually take over the San Diego diocese when Bishop Robert Brom retires.
In 2007, Brom oversaw a $198.1 million settlement with 144 people who said they were sexually abused by priests, at the time the second-largest abuse settlement since the scandal broke out in the United States in 2002.