The team also announced Matt Barkley is expected to start at quarterback with Allen out, which will make him the Bills' fourth different starting signal-caller this season.
Peterman threw for 188 yards with zero touchdowns and three interceptions in a 41-9 loss to the Chicago Bears on Sunday.
In eight career games, including four starts, Peterman has three touchdown passes and 12 interceptions.
Allen suffered damage to the ulnar collateral ligament in his right elbow against the Houston Texans in Week 6. The injury has cost him the past three games, and it will cost him a fourth Sunday.
The 22-year-old said he viewed it as a "blessing in disguise" and could use it as an opportunity to learn from Anderson.
He was named Buffalo's starter in Week 2 and has completed just 54.0 percent of his passes for 832 yards and two touchdowns with five interceptions plus 155 rushing yards and three rushing scores in six games. The Bills are 2-7.
Buffalo thought enough of Allen to trade up and pick him out of Wyoming with the seventh overall selection in the April draft. Even though he has struggled, there is still plenty of time for him to develop. Of course, getting back on field to work through those growing pains would help.
Without Allen on Sunday against the Jets, the Bills will turn to Barkley despite his limited experience in the Buffalo system and as an NFL starter.
The 28-year-old former USC standout is 1-5 as a starter, and he has thrown for 1,911 yards and eight touchdowns with 18 interceptions in 11 games.