"They're not done," coach Marc Trestman said. "They're going to be back."
Pro Bowl cornerback Charles Tillman also left the game with a knee injury as Chicago (4-3) lost for the third time in four games.
The Bears are off this week, but with the injuries mounting, their season could be slipping away from them. The defense has been hit particularly hard in recent weeks, and now, the offense is without its leader.
Cutler came up clutching the top of his left leg following a sack by 333-pound nose tackle Chris Baker with about 10 minutes left in the first half. He stayed down for a few minutes and eventually limped off the field.
"They said this is a minimum four weeks and then we'll evaluate it week to week," Trestman said. "Based on the history I talked to the doctors this morning of this injury, four weeks is a reasonable start and that it would be week to week."
Josh McCown entered in the second quarter, seeing his first game action since the 2011 season. He completed 14 of 20 passes for 204 yards, including a 7-yard touchdown pass to Martellus Bennett that gave his team a 41-38 lead with 3:57 to play. McCown looked understandably rusty in his first few plays, but he put Chicago in position to win the shootout with the Redskins.
The Bears will need more of the same if they're going to have a chance of winning their next game at Green Bay on a Monday night following the bye, not to mention beating Detroit the following week.
They didn't fare well the last time they went an extended period without Cutler. After he broke his thumb two years ago, the Bears dropped five of six after a 7-3 start in a collapse that cost general manager Jerry Angelo his job.
Back then, Caleb Hanie struggled in a big way. The Bears then turned to McCown, who had been coaching high school football in North Carolina, late in the season. They have more weapons now with Brandon Marshall, Alshon Jeffery and Bennett, not to mention a rebuilt offensive line and a system that's geared more to quick, high-percentage passes than what they were running under Mike Martz.