"Well, I don't know how long he is out but it's tough,'' offensive coordinator Mike Tice said Tuesday. "It's too bad because he was starting to come on.
Jeffery suffered the injury in Sunday's 41-3 victory over the Jaguars. He stands second on the team in receptions with 14 for 184 yards and two touchdowns.
"Injuries are part of it," coach Lovie Smith said. "He'll be back before we know it.''
Injury update, part II: Bears linebacker Blake Costanzo underwent thumb surgery and was held out of practice Tuesday. The plan is for the special teams ace to be back Oct. 22 when Lions visit Soldier Field.
Costanzo went through two games playing with one good hand before having surgery with the benefit of the off week to give him extra time to heal.
The Bears signed Costanzo to a $1.965 million, two-year contract with the plan being for him to lead the special teams unit. He has four tackles on special teams, three solo, tying him for second.
Day of rest: Veterans Cutler, Brian Urlacher, Lance Briggs, Julius Peppers and Roberto Garza were among the players rested during Tuesday's abbreviated practice. The Bears typically rest players during the off week. The Bears will practice Wednesday before an extended weekend. They will return to practice Monday.
Extra points: The Bears put tight end Brody Eldridge and cornerback Jerome Murphy through a workout on Tuesday, according to an NFL source. Eldridge was a fifth-round pick of the Colts in 2010 and the Rams selected Murphy in the third round that same year. Eldridge recently completed a four-game suspension for violation the league's policy on performance-enhancing drugs. ... Bennett (hand) practiced Tuesday while rookie fullback Evan Rodriguez (sprained MCL) remained sidelined. … Defensive back Sherrick McManis (undisclosed) did not practice Tuesday. … The Bears dumped running back Harvey Unga from the practice squad and signed receiver Kamar Aiken, who last played for the Bills. Aiken played at Central Florida, the same school that produced Brandon Marshall.
Brad Biggs contributed to this report.