The closed-door vote by the judicial affairs committee was a simple recommendation to parliament, which will make a definitive decision on June 11th, according to spokesman Jaume Duch, confirming a report by the BBC.
A source close to the matter said the committee vote was "very unfavourable" toward Le Pen.
French authorities asked the European Parliament in November to lift Le Pen's immunity as a lawmaker so that she can be prosecuted for remarks made in a speech to her FN party supporters in December 2010.
In the speech Le Pen denounced the holding of Muslim prayers in the streets of France -- where a dearth of mosques has forced many to pray outside -- saying: "For those who like to talk about World War II, to talk about occupation, we could talk about, for once, the occupation of our territory.
"This is an occupation of parts of our territory. ... There are no armoured vehicles, no soldiers, but it is an occupation all the same and it weighs on people."
Prosecutors in Lyon, where the speech took place, opened an investigation into the remarks for "inciting racial hatred" in January 2011 following a complaint from an anti-racism group.
As with many national parliaments, members of the European Parliament enjoy immunity from criminal and civil liability for opinions expressed as part of their duties, unless the chamber votes to lift the immunity.
Florian Philippot, FN vice president, told AFP that he would wait for the full parliament's vote, adding that it would be unheard of if Le Pen lost her immunity "for having spoken the truth about the (Muslim) prayers in the streets which still take place.... The French do not like when people hide the truth from them."
Le Pen took over the Front National from her father, party founder Jean-Marie Le Pen, who has several convictions for racism and anti-Semitism.
Marine Le Pen, who was first elected to the European Parliament in 2004, won 18 percent of the vote in the first round of France's presidential election in April 2012, the party's highest-ever score.