Kittle suffered the injury while trying to secure a deep throw from Jimmy Garoppolo in the first quarter.
Rapoport also reports the second-year pro didn't suffer any tears or structural damage. NBC Sports' Matt Maiocco adds that Kittle is expected to miss a couple weeks.
Kyle Shanahan said in his postgame press conference he'd be surprised if Kittle is available next week.
"It's going to be some time, I don't know how long. I have a feeling it's going to be some time," the head coach said, adding that he hasn't received an official update from team doctors.