Ford, who had no stats Sunday in 21 snaps, ranks third on the team with 6.5 sacks.
“Any time you have a hamstring strain, there is concern it could be a couple of weeks,” coach Kyle Shanahan said Monday.
The 49ers hope tight end George Kittle can return this week. Kittle has missed two games with knee and ankle issues.
“I know it was enough to keep most people out for some time, which is has for George,” Shanahan said. “He’s missed two games now, and I know it will go down to the wire again this week. But hoping this week will be different.”