In a statement on Friday France's interior ministry announced that it will explore "all legal means" to ban the comedian's "public meetings", which "are no loger part of the creative dimension but contribute ... to increasing the risk of disturbance to public order".
Dieudonné, as he is generally known, "addresses in an obvious and insufferable manner the memory of victims of the Shoah", the statement said.
Interior Minister Manuel Valls strongly condemned his "racist and anti-Semitic statements".
The comedian, who has stood as a candidate for his Anti-Zionist Party in the 2012 general election, usually performs to packed houses at the Main d'Or theatre, which he runs, in Paris.
He is currently facing legal action for failing to pay a fine for an anti-Semitic video posted on the internet and owes a total of 36,000 euros in accumulated fines.
State-run radio Radio France last week announced its intention of suing Dieudonné for remarks in his current show about one of its presenters, Patrick Cohen, who questioned the wisdom of inviting him and several other controversial figures to appear on television.
During his performance the comedian implied that it was shame that Cohen's forebears escaped the Nazi gas chambers and that he would do well to leave the country "if the wind changes".