The bomber blew up a vehicle packed with explosives outside a rebel command centre in the village of Susian, eight kilometres northeast of Al-Bab, the Syrian Observatory for Human Rights said.
The blast devastated the twin command posts and also seriously wounded a large number of fighters, the Britain-based monitoring group said.
It had earlier said that 42 people, mainly rebels, had died, but later clarified to say the majority of those killed were civilians.
"(Abu Bakr) al-Baghdadi's dogs could not bear their huge loss, and their suicide bombers have begun to take revenge," said field commander Abu Jaafar of the Mutasem Brigades.
He said rebel fighters, Turkish soldiers, and civilians from Al-Bab had called a meeting in Susian "to organise a security apparatus and set a plan for rebuilding al-Bab."
"This information reached the (IS) sleeper cells, which prepared a car bomb" that detonated at Susian around 0800 am (local time), he told AFP.
Separately, two Turkish soldiers were killed in a suicide attack in Al-Bab today as they were carrying out road checks, Prime Minister Binali Yildirim said.
The strategic town, just 25 kilometres south of the Turkish border, was the jihadists' last stronghold in the northern Syrian province of Aleppo.
Turkey sent troops into Syria last August in an operation it said targeted not only IS but also US-backed Kurdish fighters whom it regards as terrorists.
With its support, the rebels launched an offensive to take Al-Bab last year.
Turkish Defence Minister Fikri Isik said yesterday that its rebel allies now had "near complete control" of the town.
The town was also seen as a prize by Syrian President Bashar al-Assad's forces, who had advanced to just 1.5 kilometres from its outskirts in recent weeks.
Yesterday afternoon, an AFP correspondent heard intermittent gunfire as rebel units continued to clear the heavily damaged town.
The battle against IS around Al-Bab is just one front line in Aleppo province.
West of the second city, which government forces took full control of in December, fighting flared with rebels in its western suburbs even as peace talks got under way in Geneva.
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