Norman confirmed the four-week timeline on Friday via Twitter: "But 4weeks."
NFL Network's Ian Rapoport earlier reported that Norman is out four weeks with a rib fracture and small puncture in his lung, per sources informed of the situation.
Norman sustained the injuries while making a tackle in the 29-20 loss to the Kansas City Chiefs on Monday night.
"There is a concern there," Redskins coach Jay Gruden told reporters Tuesday. "I don't know where it is, how severe the pain is for him, but when you have to play bump and run, you have to tackle and all that stuff, I think it will be a pain-tolerance during (the game). We have got to make sure it's healed enough where he can play and be effective and not do more damage to it. The initial report was a fractured rib will be two to four weeks."
The Redskins have a bye this week, so a four-week absence would place Norman's return in Week 9 against the Seattle Seahawks on Nov. 5.
Norman, signed to a five-year, $75 million deal by Washington in April 2016, had not missed a game since joining the Redskins.
The 29-year-old Norman has 14 tackles, four passes defensed and two forced fumbles through four games this season. He appeared in all 16 games in 2016 for the third time in his first five NFL seasons, registering 67 tackles and three interceptions.
Norman fractured his rib trying to make a tackle on Chiefs tight end Travis Kelce after a catch and run. Norman was replaced by Quinton Dunbar.
"I just have to take my time and have faith," Norman said after Monday night's game. "I wanted to go out there, but do I more help the team or hurt the team if I can't really run and breathe hard?
"It was tough. I told them to put me out there as a decoy. I was coming up with a whole bunch of things, let me get back out there. I just wanted to give (teammates) juice just, just like they give me."