Justice ministry spokesman Pierre Rance said the request was sent to European Parliament President Martin Schulz late last month.
A source close to the matter said the request was related to an ongoing judicial probe into remarks made by Le Pen in a speech to supporters of her Front National party in December 2010.
Denouncing the holding of Islamic prayers on the streets of France, where there are not enough mosques with the capacity to hold the number of practising worshippers, Le Pen said: "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 in January 2011 into the remarks, following a complaint from an anti-racism group that she was inciting racial hatred.
Like 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.
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, the party's highest-ever score.