Benjamin, also a wide receiver, hurt the knee on a return with 2:34 left in the third quarter of Sunday's 23-17 loss to the Kansas City Chiefs.
Browns coach Rob Chudzinski said the injury took place when Benjamin planted and twisted as he headed upfield.
Benjamin averaged 11.7 yards per punt return and scored on a 79-yarder against the Buffalo Bills on Oct. 3, when he set a team record with 179 yards in returns.
"Travis obviously is a big part of what we do and has been in terms of return game," Chudzinski said Monday. "He's explosive and has the speed and ability to make a big play."
The Browns will turn to Davone Bess as their primary punt returner. Bess, though, had a crucial fumble in the loss to the Chiefs.
Chudzinski said another option would be to use Joe Haden, though he would prefer not to use the talented cornerback on special teams.