The deal, signed by former Italian culture minister Dario Franceschini, was "unbelievable", current junior culture minister Lucia Bergonzoni, a member of the far-right League, told the Corriere della Sera newspaper.
"To give the Louvre all these paintings would put Italy on the margins of a major cultural event," she said.
The Louvre is planning the show for 2019.
The Renaissance master was born in Italy in 1452 and died in France in 1519.
"Leonardo is Italian, he only died in France," Bergonzoni said.
She called for the whole deal to be revised.
"Where museums' autonomy is concerned, national interest cannot come second," she said. "The French cannot have everything."
Italy would miss Raphaels
Italy would lose out on another aspect of the agreement if it is scrapped, however.
The quid pro quo provides for the Louvre to loan works by Leonardo's contemporary, Raphael, to Rome's Scuderi del Quirinale museum for a 2020 exhibition to mark 500 years since his death.
Bergonzoni, whose ultra-nationalist party is in coalition with the anti-establishment Fice Star Movement, was not fazed by that.
"Most of Raphael's works are already in Italy," she said. "What's more, Paris says that only 'movable' paintings can come to us, without specifying which ones."
Mona Lisa and Les Bleus
The Louvre's most famous exhibit is Leonardo's Mona Lisa, which attracts snap-happy crowds every day.
There was a storm on Twitter when the museum featured the painting in a message of congratulation to France's football team for winning the World Cup in July.
Italian tweeters complained about "appropriation", some apparently believing the painting was stolen by Napoleon when his troops invaded their country.
"Point of information, la Gioconda [Mona Lisa] was sold by Leonardo de Vinci to King François I," the museum replied in a tweet in Italian.