The oft-injured Rice was hurt during the Seahawks' 14-9 win over St. Louis Monday.
The 27-year-old made 15 catches for 231 yards and a team-leading three touchdown grabs this season.
Rice, in his third season with Seattle, previously missed time in 2011 with concussion symptoms and played just six games after hip surgery in 2010 while a member of the Minnesota Vikings.
Another former Vikings receiver, Percy Harvin, is expected back with the 7-1 Seahawks soon after missing their first eight games, also after undergoing hip surgery.
Celebrity Families of 2014 [PHOTOS]