Asked on which hit Rogers sustained the concussion, Packers coach Mike McCarthy said: "I think it was the one at the end of the game."
Rodgers was 27 of 46 for 293 yards with one touchdown pass and the one interception. The Packers' last seven possessions resulted in four punts, two missed field goals and the turnover.
Rodgers was one of a handful of Packers players who were hurt Sunday: linebacker Clay Matthews strained his left hamstring; tight end Donald Lee hurt his shoulder; tight end Jermichael Finley was carted off the field with a bad knee after Green Bay's second offensive play and will have medical tests Monday; defensive lineman Ryan Pickett left two plays later with a sprained ankle; and safety Derrick Martin sprained a knee.
The Milwaukee Journal-Sentinelreported after the game that Finley suffered a hamstring ligament injury early in the first quarter, a problem Finley said he had before. He watched the second half on crutches from the sideline.
Matthews reportedly had a tight and possibly pulled hamstring, but the injury isn't believed to be overly serious, the Journal-Sentinel reported.
The Packers didn't specify whether the injuries were on a player's left or right side, but Matthews had ice wrapped around the back of his left leg on the sideline.
Lee left after catching a 5-yard touchdown pass from Rodgers about six minutes into the game.
Finley tried to make a tackle on the second play, after Redskins safety Kareem Moore picked up a fumble and returned it.
"I was like, 'Should I really tackle this guy, because something crazy is about to happen?' In the back of the mind, I was like, 'I shouldn't do this.' And I went after it. And something in the back of my leg popped," Finley said.
He was attended to on the field, then driven away on a cart. Finley entered Sunday leading NFC tight ends with 301 yards receiving.
"The two injuries to our tight ends took us out of some packages," McCarthy said.
Two plays after Finley left, Pickett stayed down briefly, then walked off the field with help.
"As far as injuries, I think we can overcome them. We just have a lot right now," Pickett said. "We've got to get people healthy."
The Associated Press contributed to this report.