Davis will sit out Saturday's game against the Pacers as he recovers.
He said he tweaked his hamstring while guarding Indiana's Darren Collison early in the second quarter. Collison drove past Davis en route to knocking down a 13-foot floater.
Davis said he felt a "little pinch" after the play. He turned the ball over on the next possession and was replaced by Jeremy Lin with 9:10 to go in the second quarter. The substitution was planned, but Davis called it "perfect timing."
Instead of traveling to Indiana, Davis will remain in New York on Saturday to receive treatment on the injury. He is optimistic about returning in time to play Tuesday against Toronto.
"It's nothing serious," Davis said. "I should be all right in a couple of days."
Davis sat out the first seven weeks of the season with a back injury. He is serving as the backup for point guard Lin.
Davis is averaging 4.5 points per game this season, as well as 5.6 assists in 17.3 minutes.
The injury comes at an unfortunate time for Davis. The 32-year-old said he was just starting to get into game shape.
"It's very frustrating," Davis said. "We were in a good groove and I was in a good groove, finally."
On Friday, Davis came out strong, scoring seven points and handed out an assist in 6:56 of game time before exiting with the injury.
Earlier Friday, new Knicks coach Mike Woodson said he was planning to keep Lin as the starting point guard, with no plans for Davis to usurp the role.
"Right now Jeremy Lin is our starting point guard and Baron is backing him up," Woodson said during his pregame chat with reporters. "That's the way it's going to be the rest of the season pretty much unless somebody gets hurt. I like that rotation. We also can move (Iman Shumpert) over to one sometimes. That's kind of the rotation I'm looking at right now."
Ian Begley is a regular contributor to ESPNNewYork.com.