The France striker suffered the injury against Fulham on Saturday, and has told L'Equipe that he may be finished for the campaign.
"I'm on crutches, I don't feel good," he said. "I don't know whether I will have this ankle problem for days, weeks or months. But it's going to be difficult for me to play again before the end of the season."
He added: "It's tiresome to get all these injuries. They all come along just when I'm starting to get a run going. It is hard. It sucks. But I'm trying to think positive."
Saha's injury means manager David Moyes has just one recognised striker to call on in Jermaine Beckford, with Yakubu out on loan at Leicester.
Source: PA
Source: PA