The far-right presidential candidate is on a two-day tour of Lebanon where she is courting Franco-Lebanese votes ahead of the first round of French elections on April 23.
Le Pen told reporters that she was surprised by the requirement. But a spokesman for the Grand Mufti said Le Pen had been informed of the need to wear a head covering before the meeting.
Le Pen said she had met the Grand Mufti of Al-Azhar during a visit to Egypt in 2015 without covering her head.
"I met the grand mufti of Al-Azhar," she told reporters. "The highest Sunni authority didn't have this requirement, but it doesn't matter."
"You can pass on my respects to the grand mufti, but I will not cover myself up," she insisted.
Le Pen has been outspoken in her opposition to the headscarf and has stated that she would ban all religious symbols in public places.
A spokesman for Lebanon's Sunni religious leader, Grand Mufti Abdel Latif Derian, told CNN that Le Pen had been informed of the need to wear a head covering prior to the meeting.
Burqa, niqab banned in France
"I personally greeted her at the door of the Edict House and wanted to hand her a white headscarf that was in my hand, she refused to take it," Khaldoun Awas explained.
"I urged her to put it on, she refused and said she would not put it on and walked out without attending the previously agreed upon meeting with the Mufti. The Edict House regrets such inappropriate behavior at such meetings."
Shortly after the incident, Florian Philippot
, the vice president of Le Pen's Front National Party tweeted: "In Lebanon, Marine refuses to wear the veil. A beautiful message of freedom and emancipation sent to women in France and the world!"
The burqa and the niqab, a full face veil worn by some Muslim women, have been prohibited in public areas in France since 2011
. Headscarves and other "conspicuous" religious symbols were banned from French schools in 2004
Mayors in some French towns sparked controversy and protests last summer when they banned women from wearing burkinis
on beaches in the wake of the Nice terror attack. The ban was later overturned