The Dolphins will turn to Jacoby Brissett at quarterback in his place.
Tagovailoa had already been ruled out for Week 3 due to the broken ribs he suffered last week.
Tagovailoa, 23, was selected with the No. 5 overall pick out of Alabama in 2020 by the Dolphins. He signed a four-year, $30,275,438 rookie contract that included a $19,578,501 signing bonus.
The contract includes a fifth-year option for the Dolphins to pick up for the 2024 season.
In 2021, Tagovailoa has started two games and completed 17-31 pass attempts (54.8 percent) for 215 yards, one touchdown and one interception. He’s also rushed for a touchdown.