Beckham was downgraded on Saturday, and he did not travel with the team.
The injury was disclosed on Friday, when Beckham was a limited participant in practice. But the Giants didn't believe it was serious at the time and didn't even give him an official injury designation for the game.
Coach Pat Shurmur said he believed Beckham would play.
"We just gave him a little time," Shurmur said after Friday's practice. "He's going to be fine."
Beckham disclosed the injury during the most recent episode of his Facebook docuseries "I Am More: OBJ" and said it originally occurred on the final play when he was leg-whipped against the Philadelphia Eagles on Nov. 25. It was in this episode that Beckham detailed the investment he makes in himself by stating he spends "over $300,000" on his body in the offseason.
His absence leaves the Giants (4-8) without their leading receiver against the Redskins. Beckham has 77 catches for 1,052 yards and six touchdowns this season.
Bennie Fowler, Russell Shepard and Corey Coleman should play bigger roles without Beckham in the lineup. Tight end Evan Engram is also expected to return after missing the past two games with a hamstring injury.
Beckham was a full participant in practice on Wednesday and Thursday. It wasn't until Friday that the quad seemed to become more of a problem.
It wasn't until he was reexamined Saturday morning that the determination was made that he couldn't play this week against the Redskins.