Anthony Montgomery is scheduled to have surgery on his fractured right hand on Monday.
He said he would be sidelined 2-4 weeks.
Montgomery suffered the injury making a tackle during Saturday's intra-squad scrimmage at Redskins Park.
He is scheduled to have surgery on Monday. He is expected to be fitted for a protecting cast that will cover his entire hand and eventually allow him to play as the injury heals.
"It's kind of frustrating, but I am just thankful that [the injury] is nothing major like a knee or a shoulder," Montgomery said. "I can still come back during the preseason. If it was half a season, or alls season, it would be a lot worse.
"You never want something like this, but I can come back with a speedy recovery, so I am thankful for that."
Montgomery is the fourth defensive lineman to suffer a significant injury in training camp.
Phillip Daniels suffered a knee ligament injury and Alex Buzbee suffered a ruptured Achilles on the first day of training camp. J.T. Mapu suffered a knee ligament injury and was waived with an injury settlement.
"Going into this game, you know injuries are a possibility, so you have to expect things like this to happen," Montgomery said. "You never want it to, but when it does, that's why you work hard in the offseason--to be prepared for situations like this."
The Redskins' injury list is a long one.
Players sidelined for Sunday's practice included Devin Thomas (hamstring), Malcolm Kelly (hamstring), LaRon Landry (hamstring), Anthony Mix (hamstring), Chris Wilson (calf) and Rian Wallace (fractured hand).
Meantime, Rocky McIntosh, Carlos Rogers, Kareem Moore and Erasmus James continue to rehab knee injuries on the sidelines.
Head coach Jim Zorn admitted that it was difficult to run Sunday's practice with so many players banged up.
"The rotations get messed up, the healthy players have to work harder, and you cannot evaluate the players that are injured," he said.
He added: "Sometimes players will pull themselves out of practice when they are sore, but not injured. I have not seen any of that [here] and players are continually pushing through the soreness.
"That is a sign of a mature and veteran team that really wants to be playing."