Defensive tackle Anthony Montgomery broke a bone in his right hand during Saturday's intra-squad scrimmage at Redskins Park.
Montgomery is scheduled for surgery on Monday. He is expected to be sidelined about 10 days, team officials said.
Montgomery is expected to be fitted for a cast that covers his entire hand. In time, he could be cleared to play with the protective cast.
"What we'll do is we'll let him rest it and get the swelling out of it," Zorn said. "And then we'll probably put him in one of those casts that look like a boxing glove."
The injury occurred early in the scrimmage. Montgomery left the practice field, but later returned and watched the rest of the scrimmage from the sidelines.
Montgomery, entering his third NFL season, was one of three defensive starters to see action. The others were Reed Doughty and Marcus Washington.
Montgomery emerged as a reliable defensive lineman in 2007, starting 16 games and recording 47 tackles and a half-sack. It was his first full year as a starter.
Linebacker Rian Wallace also suffered a fractured right hand during the scrimmage. Like Montgomery, he is scheduled for surgery on Monday.
Wallace is expected to be sidelined 10 days, team officials said.
Players who sat out the scrimmage due to injury were Devin Thomas (hamstring), LaRon Landry (hamstring), Malcolm Kelly (hamstring), Kerry Brown (shoulder) and J.T. Mapu (knee).
Anthony Mix played in the scrimmage despite a mild hamstring injury. He appeared to aggravate the injury and was sent to the athletic trainer's tent for evaluation.
Mix sat out the rest of the scrimmage with an ice pack around his upper leg.