The team initially said the surgery would take place Tuesday but quickly changed that statement to say a date hasn't been set. Head coach Lovie Smith insisted Monday that the plan is for Cutler return before the playoffs.
"He'll be out an extended period of time," Smith said. "The plan now is for him to have surgery on the thumb soon, and I can't tell you exactly how quick, but as soon as possible. Not today, but hopefully fairly quickly we can have surgery on the thumb.
"And I also said, the plan is to get him back at the latter part of the regular season. This is what I wanted to know, 'Was it a season-ending injury?' No. From what I've been told right now, we can expect him back at the end of the regular season. For me, that's enough to go on."
Cutler injured the right thumb while trying to make a tackle on Antoine Cason, who intercepted a pass with just less than 10 minutes remaining in the fourth quarter. Cutler continued to play after the injury, completing his final two passes for 24 yards in the team's final drive.
"It's devastating," linebacker Brian Urlacher said. "It's horrible, and I felt worse for him than I did for us. It stinks for us because he's having such a great year. He's our leader. He's the guy we turn to for pretty much everything."
The Bears also announced that long snapper Patrick Mannelly ruptured the anterior cruciate ligament in his knee and is out for the year.
While Smith believes Cutler could return before the postseason, sources said Cutler will likely miss the final six regular-season games.
"I'm not going to play doctor right now," Smith said on WBBM radio in Chicago when asked how long Cutler will be sidelined. "We're going through the process."
With Cutler out, the attention turns to backup Caleb Hanie, who will take over as the starter. A four-year veteran, Hanie played in two games in 2010, completing 8 of 14 passes for 66 yards and an interception.
Hanie also filled in for Cutler in the NFC title game, and hit 13-of-20 for 153 yards a touchdown and two interceptions in a loss to the Green Bay Packers.
"Caleb has been around here a long time, and our football team feels comfortable with him leading us," Smith said. "Don't feel sorry for us, or anything like that. We have a lot of things in place. We're losing and we're going to miss a great player for a period of time, but offensively we're going to rely on our running a game a little bit more. We have a great defense and special teams."
Rookie Nathan Enderle is the Bears' only other healthy quarterback, so Smith said the plan is to sign another veteran quarterback.
"The plan is for that. With Jay being out for awhile, we need another quarterback on our roster," Smith said. "The plan is to look for a veteran, preferably, to come in and help us."
It's expected the Bears would consider quarterbacks with experience playing in the system of offensive coordinator Mike Martz.
One who will not be in the running is Kurt Warner. The former Rams and Cardinals QB tweeted that he was "bummed" for Cutler, but added, "Been there 2 many times & he was playing great fball! Yes, I know & luv offense but NO I am NOT unretiring!"
Another name that comes up in any discussion of need at quarterback is familiar to Bears fans -- Brett Favre. There is no indication that the Bears are interested, but Cutler and Favre share the same agent, Bus Cook.
Former Jaguars quarterback David Garrard -- with no experience in Martz's system -- also seemed like a logical option, but he's just starting rehabilitation from back surgery and won't be able to undergo any contact for at least three weeks, according to a source.
Urlacher said the team "can live with" Hanie and even Enderle.
"With the way we play defense and special teams and the way we run the football, we can win with those guys at quarterback," he said. "We're not happy about what happened, but we're not going to panic, as players. I don't know what the organization is doing, but our coaches won't panic. We'll settle down, get Caleb in there, get his reps and all that good stuff, but we're not panicking right now."
The Bears opened a roster spot for a veteran QB, releasing defensive end Mario Addison on Monday.
The Bears have won five games in a row to improve to 7-3. It's possible Cutler could rejoin the team in time for the playoffs.
Smith said the Bears' strategy won't change.
"Running game, play from our quarterback position, outstanding defensive play, special teams," he said. "We've been in this situation before. So again, it's unfortunate, we don't know exactly how long Jay will be out, but while he's out the ship will keep moving."
ESPNChicago.com's Michael C. Wright, Jeff Dickerson and The Associated Press contributed to this report.