The French striker, who plays for Everton, was told "go back to France ya f****** n*****" after the account of a fan was allegedly accessed without permission.
It emerged on the day politicians called for an inquiry into racism in football, claiming the Football Association and individual clubs were "dragging their feet" over the issue.
Saha, 33, retweeted the offensive message, received on January 4, and added his own comment in reply, saying: "Don't attached (sic) urself with the club. U disgrace."
The account which sent the message has now been deleted and Saha later updated his 80,000 Twitter followers telling them an investigation was carried out and the offensive tweet was sent without the user's authorisation by a work colleague.
Saha, who has also played for Manchester United, Fulham and Newcastle, also said the abuser had been suspended from his job.
A spokesman for Everton said officials and police were aware of the incident and a "thorough and proper" investigation was taking place.
Race rows have plagued the game in recent weeks, with England captain John Terry accused of racially abusing QPR defender Anton Ferdinand - a claim he strenuously denies - and Liverpool's Uruguayan star Luis Suarez receiving an eight-match ban for racially abusing Manchester United defender Patrice Evra.
On Friday Oldham defender Tom Adeyemi broke down in tears after apparently being subjected to racist abuse from a supporter in the stands at Anfield during an FA Cup clash with Liverpool.
A 20-year-old man was arrested and bailed for allegedly racially abusing the player at the match.
Mike Hancock, Liberal Democrat MP for Portsmouth South and a member of the All-Party Football Group, said on Monday: "An inquiry will be welcome, but it has to have real teeth.
"The abuse is completely unacceptable."