Cutler managed to finish Sunday's game, throwing for 286 yards and two scores in Chicago's 31-20 win. He also met the media after the contest and gave no indication of an injury, which likely occurred while he was trying to make a tackle following an interception by Antoine Cason in the fourth quarter.
However, reports began to surface Sunday night and Smith, in an interview with WBBM radio on Monday morning, confirmed the injury that could keep the quarterback out for the rest of the regular season.
"Jay does have a right thumb fracture," Smith said on WBBM. "We took x-rays [Sunday] night and he'll be seeing a specialist [Monday] and we'll be able to tell you a little bit more after that."
Smith is expected to address the media later Monday during his usual day-after game press conference.
The Chicago Tribune reported Sunday night that Cutler will undergo surgery.
Cutler has played well this season, leading the Bears on a five-game winning streak and a record of 7-3. He has thrown for 2,319 yards with 13 touchdowns and just seven interceptions.
Caleb Hanie will take over under center for the Bears, starting with next Sunday's game against Oakland. Hanie has yet to throw a pass this season, but is best remembered for replacing an injured Cutler in last year's NFC title game against Green Bay.