A's manager Bob Melvin made the announcement after a 12-4 win over Detroit on Thursday, a day after Anderson awkwardly fell off the mound. Melvin said he doesn't yet know whether Anderson would be available if Oakland reaches the postseason.
The Athletics are tied with Baltimore for the AL wild-card lead.
Anderson is 4-2 with a 2.57 ERA in six games.
Melvin had previously said Anderson would miss one start and that Dan Straily would take his spot.