Tagovailoa was limited in practice throughout the week, and coach Brian Flores said he is dealing with discomfort gripping the ball. He originally injured the finger during Miami's loss to the Buffalo Bills in Week 8 but was able to finish the game.
Speaking with local media earlier in the week, Brissett said he wouldn't change anything about his preparation for Thursday's game, which is his fifth start of the season.
"It doesn't matter," he said. "Whenever my time is called, I know and I trust in myself that I'll be ready to go."
Entering Thursday, Brissett had played in six of the Dolphins' nine games this season, completing 64% of his passes for 1,127 yards and five touchdowns against four interceptions. He also had run for 64 yards and a touchdown on 17 carries.