Norris picked up the injury in his club's 3-3 draw with Blackburn Rovers last weekend.
Warnock told the Yorkshire Evening Post: "It's another blow and I'm really disappointed for him. He's had a great start to the season.
"He'll be looking at three to four weeks so it's not long-term but we've already lost Paul Green and we've got Michael Brown struggling with a hamstring strain. We're looking thin in that area now."
The 31-year-old was a summer signing from Portsmouth.