Tim Stauffer was slated make his first start of the season in Correia's place.
San Diego manager Bud Black said Correia's brother died on Saturday, and Correia flew from Houston to California on Sunday morning.
Black had no other details. He said the team would consider later in the week whether to place Correia on the bereavement list. The Padres open a three-game series in San Francisco on Tuesday.
"It's still so early to know how this is going to sort out," Black said. "I think things will become more clear once we get to San Francisco, how Kevin is doing and what we need to do."
Correia (4-2, 3.97 ERA) is scheduled to pitch again Saturday against the Los Angeles Dodgers.