The Redskins initially designated Rice as "waived-injured." He was moved to IR on Monday after clearing waivers.
The Redskins replaced Rice on the roster by signing defensive lineman Jeremy Towns, an un-drafted rookie from Samford.
Rice was hurt last week when he fell on his shoulder while trying to catch a pass in the end zone.
Rice was undrafted out of UNLV. His father played 20 NFL seasons and is in the Hall of Fame.