Gonzalez left in the fifth inning of Tuesday's game against Arizona when his finger again swelled.
"I try to stay in there, but it gets to the point where I can't grip a bat. It gets so big, I can't fit into a batting glove," Gonzalez told reporters after the game.
He missed three games in late May because of swelling in the same finger. The 28-year-old Gonzalez played in just 19 games after the All-Star break last season because of a sprained right middle finger.
Gonzalez is hitting .255 with eight homers and 35 RBIs this season. It's his worst batting average since his rookie season with the Oakland A's in 2008 (.242).
The break will give Gonzalez a chance to rest not only his ailing finger but also a balky left knee that's given him trouble at times.
The Associated Press contributed to this report.