According to Redskins head coach Jay Gruden, the non-contact injury occurred after Culliver came down awkwardly while jumping for a ball.
"He hurt his knee a little bit out there," Gruden said after practice. "He jumped up for the ball, landed on it."
After undergoing an MRI, it was revealed that the injury was much more serious than Gruden initially thought.
The 27-year-old has made six starts for Washington this season, tallying 16 tackles and a pass deflection.
Culliver joined the Redskins as a free agent this offseason, signing a four-year, $32 million contract.
He played in 46 games over his first four seasons, all with the San Francisco 49ers. He missed the entire 2013 season with a torn ACL.