Ireland injured himself in the game at Southampton, coming off at half-time in the St Mary's loss.
Speaking directly after the Manchester City win, Lambert said: "It's not Stephen's arm. It's his wrist.
"I don't think it's as bad as we thought. Hopefully he will be back in a few weeks time.
"Injuries happen. It's unfortunate for Stephen and it's unfortunate for us.
"But he won't be out for the number of weeks we thought he would be."