It was thought the 49ers, coming off their bye week, might turn to Jimmy Garoppolo as the starter this week but Shanahan said the former New England Patriots quarterback is still learning the offense.
The 49ers traded a 2018 second-round draft pick to New England before the trade deadline to acquire Garoppolo.
Beathard earned his first NFL victory in Week 10 when he led the 49ers to a 31-21 victory over the New York Giants. The victory was San Francisco's first this season.
Beathard threw for 288 yards with two touchdowns and and an interception against the Giants. He also rushed for a touchdown.
In six games this season he has passed for 1,229 yards with four touchdowns and five interceptions. He is completing 54.3 percent of his pass attempts (101-of-186).