Le Pen then cancelled the meeting telling reporters: "You can pass on my respects to the Grand Mufti, but I will not cover myself up."
Representatives of the Grand Mufti told Reuters that Le Pen's aides had been informed of the requirement to wear a headscarf before the meeting.
Le Pen has been shunned by many European leaders due to her party's stance on immigration and anti-EU message.
However the French presidential candidate is visiting Lebanon in an attempt to burnish her credentials as a defender of Christians in the Middle East ahead of France's April 23 presidential elections.
During her visit to Lebanon, which began on Sunday, Le Pen has met with figures including Lebanese President Michel Aoun and Prime Minister Saad Hariri.
Hariri's father Rafik, a former Prime Minister, was assassinated in a massive car bomb attack in Beirut in 2005 which the regime of Syrian President Bashar al-Assad is widely suspected of perpetrating.
After meeting with Hariri on Monday, Le Pen expressed support for Assad stating that there was "no viable and workable solution" to the Syrian civil war beyond choosing between the Syrian President – who stands accused of innumerable war crimes – and the Islamic State group.
Le Pen is currently leading opinion polls in the presidential race. Critics say that her anti-immigrant, anti-EU stance is cover for an islamophobic and xenophobic agenda.
Rival presidential hopeful and former economy minister Emmanuel Macron visited Beirut on January 24, where he met both Aoun and Hariri. While right-wing candidate Francois Fillon, dogged by revelations his wife was paid for years with public funds for a suspected fake job as a parliamentary aide, cancelled a visit this month to Lebanon and Iraq.