The team confirmed the decision.
Beathard suffered the injury during Week 8's contest against the Arizona Cardinals after hitting his hand on a defender's helmet. He played through the injury, but according to Schefter, he has had trouble gripping a football since Sunday.
Although he will not get the start, Beathard is expected to be healthy enough to be active and to serve as the backup against the Raiders. NFL Network's Ian Rapoport reported on Thursday that the team released veteran passer Tom Savage.
Mullens went undrafted out of Southern Miss in 2017. The 23-year-old has never thrown a pass during the regular season in the NFL.
The 6'1", 210-pound Mullens—who spent last season on the practice squad—will become the Niners' third different starting quarterback of 2018. Opening day starter Jimmy Garoppolo was lost for the season in Week 3 after suffering a torn ACL.
During his four-year career at Southern Miss, Mullens completed 60 percent of his passes for 11,994 yards, 87 touchdowns and 46 interceptions. He was named the 2015 Conference USA Offensive Player of the Year as a junior, throwing for 4,476 yards and 38 touchdowns in 14 games.
Mullens was promoted to the active roster when Garoppolo was injured.