SANTA CLARA, Calif. -- As it turns out, Jimmy Garoppolo won't be the only San Francisco 49ers quarterback who has to stay in the Bay Area on the team's bye week to recover from an injury.

That's because rookie signal-caller Trey Lance suffered a left knee sprain in Sunday's 17-10 loss to the Arizona Cardinals, coach Kyle Shanahan announced Monday.

Lance had an MRI on Monday morning and isn't expected to miss much time, especially since the 49ers are on bye and won't play again until they meet the Indianapolis Colts on Oct. 24.

"It's not a long-term injury but they did say they won't be able to know until (later)," Shanahan said. "He'll have to stay here on the bye week and get treatment and everything, so we should have a good idea by the end of the next week whether he has got a chance for Indy or not. If he doesn't, they told me it should be like a one-to-two-week thing but possibly just one."

After Sunday's loss, Lance said he felt "fine" despite taking plenty of hits. Lance finished 15-of-29 for 192 yards with an interception and had 16 carries for 89 yards.

But Lance told Shanahan that he first started feeling something wrong with his knee just before he went to bed Sunday night.

According to Shanahan, neither he nor Lance could pinpoint an exact moment when the injury happened. Still, Lance will have to spend the bye week with Garoppolo rehabbing before a determination can be made on his Week 7 availability.

"I was messing with Trey and Jimmy that now Jimmy just got some company," Shanahan said. "So, they'll be here, both of them the whole week so they have the best chance to be ready for Monday when we all get back."

Shanahan has maintained that Garoppolo would return to the starting role once he returns from his right calf injury. Shanahan was again optimistic that Garoppolo's return to the lineup will come against the Colts, given that he nearly was able to play against Arizona and now has an extra week to rehab and heal.

After watching the tape of Lance's first start, Shanahan offered Monday that he was "proud" of how Lance handled himself against a good team in a tough environment. Shanahan cited how aggressive Lance was and said he was pleased with how his rookie quarterback bounced back from an early interception.

Still, none of that has changed how Shanahan views the long-term situation at quarterback even as the 2-3 Niners are mired in a three-game losing streak.

"It doesn't change my opinion big-picture," Shanahan said. "Trey definitely has the ability to help us win games. I thought he was a big part of why we had a chance to win that game yesterday. I just wish we could have played better around him, too. Not that he was perfect by any means but he gave us a very good chance to win that game and I know he will give us a chance to win a lot going forward. But it's more of a decision than just which player do you want to go with? There's a whole team here, there's a lot more that goes into it and these three losses that we've had in a row, the answer good or bad, is not just the quarterback."