The 28-year-old fractured his right thumb during the final play of the Bengals' opening drive and was replaced at the end of the first quarter by backup AJ McCarron.
"You can't go into any play thinking you're going to get hurt," Dalton said afterwards. "That's the last thing you have to think. It's unfortunate that it happened."
Sources told ESPN that the "best-case scenario" is that Dalton could return in time for the playoffs, although he will see a specialist on Monday to determine the extent of the injury.
Next up for the Bengals, who are 10-3 for the season, is a trip to the San Francisco 49ers on Sunday evening.