Norman also sustained small damage to his lung lining during the 29-20 loss, NFL Network's Ian Rapoport reported Wednesday.
With the Redskins on their bye week, Norman has not been ruled out to return when the team takes the field in Week 6 against the San Francisco 49ers on Oct. 15, according to the report.
Norman played 24 snaps, making two tackles, before taking a hit and breaking a rib in the second quarter. He is listed as week-to-week.
Norman, signed to a five-year, $75 million deal by Washington in April 2016, has not missed a game since joining the Redskins.
"That's the first time that's ever happened to where I couldn't get out there," Norman said after the game. "I just have to take my time and have faith. 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?"
Norman has 14 tackles, four passes defensed and two forced fumbles through four games this season. He appeared in all 16 games for the third time in his first five seasons in 2016, 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.
"It was tough," Norman said. "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 like they give me."