One of the clubhouse leaders for the World Series champions, the quirky Pence had played in all 162 games for the Giants the past two seasons. He hit .277 with 20 homers and 74 RBIs last year.
He was hit by a pitch from the Cubs' Corey Black and went to first base before being removed from the game.
"It didn't look good," Giants manager Bruce Bochy said. "You hate to see it but these things do happen. Guys work so hard to get ready."
X-rays showed Pence has a non-displaced fracture in his left forearm.
