Rivera said on Monday that Williams could play in Week 14 at New Orleans if the swelling subsides.
Jonathan Stewart, who had 85 yards on 12 carries against Minnesota, likely will move into the starting lineup.
Williams is Carolina's all-time leading rusher with 6,846 yards and 46 touchdowns. He has been limited to 219 yards this season, playing in only six of the 12 games because of hamstring and ankle injuries.
He had seven carries for 21 yards against Minnesota, all in the first half.
Williams, 31, has one year left on an original five-year, $43 million deal that was restructured last season to reduce his salary-cap hits to $5 million in 2013 and $6 million this season.