Benzema's lawyer Hugues Vigier said he would take legal action against Gerald Darmanin on the grounds of “false information and public insults”.
The threat comes after the footballer, who recently moved to Saudi Pro League club Al-Ittihad, posted a message online saying that he was praying “for the inhabitants of Gaza, once again victims of these unjust bombings that spare neither women nor children”.
Mr Darmanin, a member of President Emmanuel Macron’s La Republique En Marche party, responded and said the footballer should have denounced “Hamas’s terrorist attacks”.
“Everyone knows that Mr Benzema has notable links to the Muslim Brotherhood,” he said.
Mr Vigier told RMC radio station that Benzema was not linked to the Muslim Brotherhood, and said the allegation was “absolutely false”.
He said it was “incredible” that the person who oversees law enforcement could “make this kind of statement without verification”, adding that this was unacceptable.
Mr Vigier described Mr Darmanin's remarks as “nonsense” and accused him of political opportunism.
The minister's comments led to a political row in France after Valerie Boyer, a prominent senator with the centre-right opposition Republicans, called for “measures” against Benzema if the claim turned out to be true.
This would begin with the footballer losing the Ballon d’Or award he received for being the world’s best footballer last season, she said.
“Finally, we should ask for him to lose his French nationality,” she said in a post on social media platform X, formerly Twitter.
However, Aurelien Saintoul from the left-wing France Unbowed party condemned what he described as “an intolerable witch hunt” directed at Benzema.
The striker, a devout Muslim of Algerian heritage, won the Uefa Champions League five times and scored 354 goals for Real Madrid before he moved to Saudi Arabia.
Benzema, who made his debut in 2007, played 97 times for France and scored 37 goals before he retired from international football last year.