Davis was injured in the first half of the Redskins' 27-23 loss to the Giants. He needed help to the sideline and then onto a trainer's table before he was carted to the locker room.
"I didn't know what it was right away," Davis said. "I have never experienced anything like that. I was unable to walk and then I knew something really was wrong.
"I was running my route and stuck my leg in and either got stepped on or it happened naturally."
Davis was the team's leading receiver with 23 catches for 312 yards entering Sunday's game.
"I had a lot of things I wanted to do this year and I was doing it," he said. "It's very discouraging."
Logan Paulsen stepped in for Davis and had four catches for 76 yards, including a key one on a fourth-down play in the fourth quarter.
"That's why I am on the team, for this moment," the third-year tight end said. "My job is to know everything he knows."
CBSSports.com reported Sunday night that the Redskins are in talks to re-sign tight end Chris Cooley. Washington released Cooley on Aug. 28 after he spent eight years with the team.
Redskins linebacker London Fletcher, who has played in 231 successive games, left in the fourth quarter with a right hamstring injury. Coach Mike Shanahan called it a mild strain.
In the second quarter, strong safety Reed Doughty left with a left knee strain, but returned in the second half.
Information from The Associated Press was used in this report.