The 49ers said Monday night that the strain was revealed during an MRI.
Gore injured the ankle on his only carry during Sunday's 27-24 loss to the Minnesota Vikings. He left the game after a four-yard gain and did not return.
Gore was taken to the locker room on a cart, but X-rays revealed no broken bones.
The team says the injury is not related to the ankle sprain Gore sustained during his 207-yard rushing performance against the Seattle Seahawks on Sept. 20.
Gore will miss Sunday's game against the St. Louis Rams and next week's game against the Atlanta Falcons. His place in the lineup will be taken by rookie Glen Coffee, who rushed for 54 yards on 25 carries at Minnesota.
The 49ers have their bye week Oct. 18, and Gore is expected to return for their Oct. 25 game at Houston.