Le Pen says she was caught off guard by the headscarf requirement, but a spokesperson for the grand mufti says she was told about it beforehand.
Macron visited May at her Downing Street office and later met Britain's finance minister Philip Hammond, a public relations coup for the young ex-banker at a time when his campaign appears to be losing momentum.
Le Pen reportedly returned to her auto and said that she had previously met with the Grand Mufti of Al-Azhar in Egypt without wearing a headscarf.
Le Pen has made known her pro-Assad position in the past but her stance represents a major divergence from official French policy and that of Hariri, who is allied with Saudi Arabia against the Syrian leader.
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". She said Syrian President Bashar Assad was "the most reassuring solution for France", adding that the best way to protect minority Christians is to "eradicate" the Islamic State group preying on them - not turn them into refugees.
The prime minister also said that "it would be a big and serious error to link Islam and Muslims on the one hand and terrorism on the other".
The group accused investigators acting for the Paris prosecutor's office of a "media operation" created to disrupt Le Pen's campaign ahead of a presidential vote in April.
She is now at the centre of a fake jobs corruption enquiry in France, but is expected to win the first round of voting in presidential elections in April.
"It's because Marine Le Pen has been able to, in the last 10 years, to portray herself as the victim of the media in France", she said.
French law already bans headscarves in all classrooms, and Ms Le Pen has proposed upgrading the ban of the headwear and other "ostentatious" religious symbols to all public places.
But upon arriving for the meeting, she said she was surprised to be told a headscarf was required and refused to wear the garment.
Wednesday's detentions followed a police raid on Monday on Le Pen's National Front party headquarters on the western edge of Paris, while she was overseas.
Photos of Le Pen with Ahmed Tayeb in 2015 in Cairo show her with the cleric with her hair uncovered.
Israel, which is next door to Lebanon, expects visitors to wear kippahs - a hat that covers the top of the head - when appropriate, for example.