When she arrived at Sheikh Abdellatif Deryan's office in Beirut, the National Front candidate was offered a shawl to cover her hair.
But she promptly refused, which prompted the Sunni authority to accuse her of "improper behaviour".
Le Pen made a brief statement to journalists before leaving.
Deryan heads the Dar al-Fatwa organisation, the highest Sunni authority in Lebanon.
In a statement on Tuesday, the body said "its press office had informed the presidential candidate, through one of her assistants, of the need to cover her head when she meets his eminence, according to the protocol assumed by Dar al-Fatwa".
The body said it was surprised by Le Pen's refusal to conform to a known rule and regretted what it called "improper behaviour".
However Florian Philipot, the National Front deputy leader, hailed Le Pen's stance as "a beautiful message of emancipation and freedom sent to the women of France and the world".
Islamic dress is a hot-button issue in France, where the full-face veil is banned in public places.
The Islamic headscarf known as the Hijab is also banned in schools and public buildings, but Le Pen has said she wants to extend the ban to all public places.
Her stance however may open her up to accusations of hypocrisy as she regularly tells her supporters at rallies that foreign migrants in France should either adapt to French rules and culture or go home.
Should she have adapted to the cultural norms of where she was?
"On est chez nous, rentrez chez vous", which roughly translates as "This is our home, so go home" is frequently chanted by her supporters at rallies, a chant that has Le Pen's support.
Tuesday is Le Pen's last day in Lebanon, where she met a foreign head of state for the first time -- President Michel Aoun.
The FN leader, whose party takes an anti-immigrant stance, also met Lebanese Prime Minister Saad Hariri, a Sunni Muslim, and Foreign Minister Gebran Bassil.
Shunned by European leaders over her party's stance on immigration and its anti-EU message, Le Pen's meeting with Aoun aimed to boost her international credibility.