Northern Ireland international Carson, on loan from Ipswich, has returned to his parent club after breaking a bone in his foot in the closing stages of Saturday's home draw with Accrington.
York manager Nigel Worthington said: "He's broken his fifth metatarsal bone in his foot and is going to be out of action for the next six to seven weeks.
"It's disappointing, but we have to live with it. I've been in the game long enough to accept that these things happen.
"I'm very disappointed for the boy and ourselves. He's been doing very well for us, but the door opens for someone else now."
Midfielder Carson, 19, has made five appearances for the Minstermen, starting every game for Worthington's side since arriving from Ipswich last month.
Meanwhile, Worthington said he hoped to keep on-loan Sheffield United striker Richard Cresswell at Bootham Crescent until at least after the home game against Southend on April 20.
"Cressy is definitely with us for the trip to Northampton on Saturday and we're hopeful he'll still be here for the Southend game.
"Unless we hear otherwise from Sheffield United that should be the case."