Some 8,000 migrants have landed on Lampedusa since Tunisia's revolution in January.
"I also want to offer my support to the inhabitants of Lampedusa who have had the feeling of being completely abandoned," Le Pen told French press agency AFP.
"If I listened only to my heart, I would throw myself in the water to save them (the refugees). But we would all drown because my boat is too fragile.”
She was accompanied by Mario Borghezio, a fellow MEP from Italy's anti-immigration Northern League party, which is part of the governing coalition.
Lampedusa’s mayor Bernardino De Rubeis met Le Pen, but local MPs from the opposition Democratic Party have condemned her visit.
Protesters greeted her at the airport, holding placards reading: "Lampedusa is not racist!" and "Solidarity with the asylum seekers!" at a rally organised by Askavusa, a local human rights group.
Recent polls put Le Pen favourite for France's presidential election next year.
The French government has also urged Italy to stem the flow of migrants.