The fist, which had the word "revolution" written on it in Arabic, went up in flames as Lebanon marked its 76th Independence day amid an ongoing uprising that saw the country's prime minister Saad al-Hariri resign.
The six-metres-high fist, which had become a symbol of the protests, was erected in the square in the first days of the uprising, now in its second month.
Early on Friday, a man on a motorbike fled the scene after throwing a petrol bomb at the fist, Lebanese media reported. His identity and motives are unknown.
Video footage showed protesters in the square trying to extinguish the fire, to no avail.
Scores of Amal and Hezbollah supporters went on a rampage in Martyrs' Square on October 29, attacking protesters and their tents, while also attempting to set fire to the fist, but were unsuccessful.
On Friday, protesters reacted with anger to the destruction of the symbol.
"I just woke up to these images and video circulating, the sad part is the thugs who were forced to do this," Carmen Geha, an activist and scholar, said on Twitter.
"Our politicians will keep fighting this revolution but it's too late. Today we celebrate our independence from them, that's the a way to free the thugs too," she added.
"We will make a bigger one! This time a woman's hand," Charlotte M Karam, another scholar, replied.
Romy, a journalist, said on Twitter the arson meant that "They fear us and fear another independence".
Timour Azhari, a reporter in Beirut, said the company that made the fist was already preparing another version that would be put up later on Friday.
Source: Al Jazeera