Cribbs hurt his right shoulder while trying to make a tackle on a second-quarter punt return in Sunday's 23-3 loss to the Miami Dolphins. On Monday, coach Rex Ryan described the injury as "pretty serious."
The Jets (5-7) will miss Cribbs because he returned kickoffs and punts, lined up occasionally at wide receiver and ran their Wildcat package on offense. He rushed 13 times for 55 yards, completed two passes for 38 yards and caught two balls for six yards.
Cribbs, 30, one of the most prolific kick returners in history, signed in Week 7.
Reynaud can fill both return roles. In 2012, he became the 16th player to return two punt returns for a touchdown in the same game. Before the Titans, he played with the New York Giants and Minnesota Vikings.
He has more than 3,200 combined yards in punt and kickoff returns. He was cut by the Titans after muffing a punt against the San Francisco 49ers that resulted in a touchdown.