Osman suffered the injury in the Carling Cup win over West Ham last week but played when the teams met in the Barclays Premier League at the weekend, aided by a painkilling injection.
However, an X-ray has confirmed Osman will miss the festive fixture programme.
Boss David Moyes told the club's website: "It's an absolutely terrible blow.
"He broke his toe in the first five minutes of the Cup game but he battled on and it shows you how tough he is. He was in a bad way but still wanted to play.
"He had a scan and it showed a big crack and we think he is going to be out for between four to six weeks.
"Leon's form had been good and he has been playing a big part in everything that we have achieved recently."