The England left-back has been the Toffees' stand-out player in the last two seasons and provides a real attacking thrust down the flank.
But manager David Moyes now faces the prospect of heading to the Etihad Stadium to face the Premier League champions without his most consistent player.
"Leighton's got a hamstring injury. He felt it in the game and played on in the last 10 or 15 minutes," said the Scot.
"I felt we put in a lot of energy (in the game) but it might take its toll.
"We've got Gibbo (Darron Gibson) and Hibbo (Tony Hibbert) back and that has eased it a little bit but I am worried about Nikica Jelavic (ill) who has not trained since Saturday and on Tuesday I was not playing him."
Theo Walcott fired the Gunners into an early lead at Goodison Park before Marouane Fellaini pulled one back for the hosts midway through the first half.