The Bills are hoping Brown will miss the minimum three games, according to ESPN's Adam Schefter.
The 30-year-old didn't play in Buffalo's previous contest against the Arizona Cardinals due to an ankle injury.
The Bills placed offensive tackle Cody Ford on IR because of ankle and knee ailments. Coach Sean McDermott announced Friday that Ford would be out for the rest of the season.
Ford has started seven games for Buffalo this year. The former Oklahoma product was a second-round pick in the 2019 NFL Draft.
Brown has racked up 29 receptions for 386 yards and two touchdowns through eight games.
Buffalo has elevated wide receiver Jake Kumerow from the practice squad for Sunday's game against the Los Angeles Chargers. He'll join the wide receiving group of Stefon Diggs, Gabriel Davis, Cole Beasley, Isaiah McKenzie.