Allen is expected to miss about eight weeks but the Redskins aren't ruling him out for the season.
"We got better news after the surgery that it wouldn't be as lengthy as they typically are," Washington coach Jay Gruden said during his Thursday press availability. "That's good news. But we still have to rehab it. He's a big man and sometimes bigger guys take a little bit longer. We'll wait and see. Hopefully we see him again, but it's up to the rehab."
Teams can return two players off injured reserve during the season, which leaves the door open for a potential return by Allen.
Allen suffered the injury during the fourth quarter of Sunday's victory over the San Francisco 49ers.
The first-round pick (17th overall) out of Alabama started each of Washington's first five games and has 10 tackles and one sack.
"That's a big loss," Redskins cornerback Josh Norman said. "I won't sit up here and say it isn't. It is a big loss for us. He's one of our driving forces in the middle. He creates havoc on the field.
"It goes without saying that to not have him for a while like that is pretty big."
The Redskins filled the roster opening by promoting defensive lineman A.J. Francis from the practice squad.
Francis split last season between the Redskins' active roster and practice squad but didn't see any game action. He played in three NFL games in 2015 -- two with the Seattle Seahawks and one with the Miami Dolphins.