In an interview with the Le Monde newspaper, Le Pen called for religious headwear to be banned "in stores, on public transport and on the streets."
Asked if the ban should apply to the Jewish skullcap, known as the kippah or yarmulke, as well as Muslim headwear, she said: "It is obvious that if the veil is banned, the kippah is banned in public as well."
Le Pen, who shocked the French elite by winning almost 18% in the first round of this year's presidential vote, also repeated calls for bans on public prayers, kosher and halal foods in schools and foreign government financing of mosques in France.
President Francois Hollande denounced her comments, saying: "Everything that tears people apart, opposes them and divides them is inappropriate and we must apply the rules, the only rules that we know, the rules of the Republic and secularism."
France was on alert at home and abroad on Friday following the publication of the obscene cartoons of the Prophet by satirical magazine Charlie Hebdo on Wednesday.
Muslim leaders were calling for calm and urging militants not to defy a ban on protests in France over the cartoons.