The right-hander went on the DL with nerve irritation in his pitching elbow after appearing in two games, blowing a save and taking a loss. He threw two scoreless innings for Single-A Rancho Cucamonga on a rehab assignment.
Wilson, who saved 171 games for the Giants between 2006-12, was 2-1 with an 0.66 ERA for the Dodgers last season.
Dodgers manager Don Mattingly also announced before the game that the team optioned left-hander Paco Rodriguez to Triple-A Albuquerque. Rodriguez (0-0, 3.18) appeared in eight games with the Dodgers.