Coach Scott Linehan said Monday the team would probably sign a replacement this week, but didn't think Bennett, who could miss as many as six weeks, would be placed on injured reserve. He said surgery is not required at this time.
Bennett was injured on a 4-yard reception, crumpling to the turf on the tackle.
The Rams also could be without defensive end Leonard Little and guard Jacob Bell for Sunday's home opener against the Giants; both players have hamstring strains. Linehan said the team would know more after returning to practice Wednesday.
Rookie defensive end Chris Long fractured his right pinky but is expected to play wearing a splint. Punter Donnie Jones bruised his left, non-kicking, knee making a tackle on a return, but Linehan said the swelling was down on Monday.