The team did not disclose the specifics of Dalton's injury, but NFL Network's Ian Rapoport reported that Dalton suffered torn ligaments in the thumb on his throwing hand. Dalton is done for the season, and it is unclear at this point whether Dalton will require surgery.
The Bengals are 5-6 and have lost three games in a row following Sunday's 35-20 loss to the Cleveland Browns. With just five games remaining, the Bengals were a long shot to make the playoffs even if Dalton had been available.
Jeff Driskel, who replaced Dalton against the Browns, is expected to make his first NFL start in Sunday's game against the Denver Broncos.
Driskel was 17-of-29 for 155 yards with one touchdown and no interceptions against the Browns in the most extensive playing time of his career. For the season, he has completed 58.6 percent of his passes with one touchdown and no interceptions.
In a related move, the Bengals claimed quarterback Tom Savage off waivers from the 49ers.
The 49ers had waived Savage over the weekend, and presumably were going to re-sign him this week. But the Bengals scooped him up before the 49ers could act.
The Bengals also have quarterback Connor Cook on the practice squad.
Dalton finished the season completing 226-of-365 passes (61.9 percent) for 2,566 yards and 21 touchdowns with 11 interceptions.