The French striker was told to "go back to France ya f****** n*****" after the account of a fan was allegedly accessed without permission.
Saha responded by tweeting: "Don't attached urself with the club. U disgrace."
The incident follows the high profile affair involving Luis Suarez and Patrice Evra, for which the Liverpool striker was given an eight-match ban.
More recently, former Reds striker Stan Collymore reported racial abuse directed at him on the social networking site to the police.
A spokesman for Everton said officials and police were aware of the incident and a "thorough and proper" investigation was taking place.