Racial discrimination is illegal in France and anti-racism group SOS Racisme says it is taking legal action.
The ad was posted on Monday by Paris-based NSL Studio on jobs site Graphic-Jobs.com.
NSL Studio has apologised for the ad but offered various explanations as to why it contained the offending clause.
The company was quoted on Monday by French news website Les Inrocks as saying that the hours of work, particularly during busy periods, meant the candidate should not be someone with cultural or religious needs.
NSL Studio then tweeted that its advert had been hacked and thanked those who had brought the issue to its attention.
A statement on NSL Studio's website (in French) now says the company "distances itself totally from all racist or anti-Semitic acts or statements".
It says the person in charge of placing the advert will be questioned and appropriate measures taken if it does turn out that the ad originated with NSL Studio.
Job site Graphic-Jobs.com has expressed its "deepest apologies" for the ad, saying it goes completely against the company's values.
In a statement (in French) Graphic-Jobs.com says it will strengthen its checking systems and is consulting its legal team about the implications.
Announcing it was taking legal action, SOS Racisme lawyer Alexandre-M Braun said individuals had been reduced to their religious characteristics.
"Such and such cannot work with me because he is a Jew," he said. "It is Jews who are being described as undesirable".
An advert for a graphic design job in France has been withdrawn after it said the candidate should "if possible not be a Jew".