Gonzalez, 31, has missed the Rockies' past three games due to a shoulder injury.
Manager Bud Black said Monday, ahead of the series opener against the Giants, that neither the training staff nor Gonzalez were sure he would even be ready by the start of a weekend series Friday at Arizona, so this was the best decision. Gonzalez is expected to return next Monday.
Gonzalez is batting .221 with six home runs and 20 RBIs this season.
Anderson was placed on the DL after leaving Sunday's start after 2 1/3 innings with what was called a left hamstring cramp. Anderson had previously missed 3 1/2 weeks this season with left knee inflammation and pitched Sunday while wearing a brace over his left knee.
The Rockies have lost five straight and are in the middle of a nine-game road trip against division rivals.
Information from The Associated Press was used in this report.