It had been hoped that Baines would be able to play in the club's busy festive programme, but the hamstring problem he picked up in Saturday's win against Fulham is more severe than was originally diagnosed.
Manager David Moyes confirmed to the club's official website: "We've had the results of the scan and it looks like Leighton is going to be out for between four to six weeks.
"It's a blow because he's done so well for us. With Alan Stubbs also out, we're a little bit limited at the back.
"We've been really pleased with Bainesy and he'd looked sharp against Fulham, but this is something that happens sometimes.
"He had a bad ankle knock against Derby and before that had been in really good form."