"He [Saha] goes to a facility in France to get treatment and looked after and I think it will be two to three weeks before he is available," said Moyes.
Saha's fellow forward Anichebe, 22, has had a knee operation and will, added Moyes be out for "six weeks or so".
The absence of the strike duo will further frustrate the Scot following his side's poor start to the season.
How big a blow is the absence of Saha and Anichebe?
Everton are second-bottom of the Premier League after gaining just two points from five games, while the Merseysiders were also knocked out of the Carling Cup after losing on penalties at Brentford.
Moyes bemoaned his side's lack of cutting edge in attack following the defeat by Brentford, and French striker Saha's continued absence will be a major disappointment.
Source: BBC Sport
Source: BBC Sport