Williams hurt his left wrist in the second quarter of Sunday's victory over the Detroit Lions. He needed emergency surgery that night.
The former first-round pick started all nine games this season for Chicago, which has won four in a row to improve to 6-3.
Chicago also signed defensive end Chauncey Davis to a two-year contract. Davis had 178 tackles, 10 sacks and two interceptions in 96 games (25 starts) over six seasons (2005-10) with the Atlanta Falcons.
The Bears waived defensive end Nick Reed, who appeared in seven games for Chicago this season.