Correia's younger brother, 22-year-old Trevor Brent Correia, died from a fall off a 60-foot cliff on Saturday while hiking within the Channel Islands National Park off the Santa Barbara coastline.
Correia, who was scheduled to start Sunday in Houston, flew to San Diego and will be away from the team indefinitely.
San Diego manager Bud Black said before Tuesday's game that Correia will in all likelihood make his scheduled start Saturday at PETCO Park against the Los Angeles Dodgers.
A player who is placed on the bereavement list has to miss a minimum of three games and a maximum of seven games.
Russell arrived in San Francisco on Tuesday for the start of a three-game series against the Giants.
Russell has appeared in three games with the Padres this season and hasn't allowed an earned run or a hit in 4 1/3 innings. He has one walk and five strikeouts.
He hasn't fared as well with Portland, going 0-2 with a 9.00 ERA over his 12 innings of work.
Corey Brock is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.