Powell sustained the injury during the second quarter of Sunday's 37-17 loss to the Minnesota Vikings.
Powell and Crowell have split the rushes this season, with the former receiving one less carry (80) for 343 yards. Powell also added 11 receptions, including a 28-yard touchdown catch against the Miami Dolphins in Week 2.
The 29-year-old Powell has rushed 791 times for 3,446 yards with 15 touchdowns in 96 career contests with the Jets. He resides one yard shy of Adrian Murrell for 10th place on the franchise's rushing list.
Powell also has 264 receptions for 1,567 yards during his eight-year career with the Jets.
Rookie Trenton Cannon will assume a larger role in the running game with the 5-foot-10, 204-pound Powell sidelined. Fellow running back Elijah McGuire (foot) is eligible to come off of injured reserve in Week 9.
The Jets signed safety Ibraheim Campbell to take Powell's spot on the active roster.
Campbell, who was a fourth-round pick of the Browns in 2015, played in 37 games for Cleveland and registered 80 tackles. The 5-foot-11, 210-pound Campbell was waived/injured in November 2017.
Campbell appeared in four games for the Dallas Cowboys this season before being waived in October.