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.
Most of the dead were fighters.
There was no immediate claim for the attack but it bore all the hallmarks of IS, which had put up fierce resistance in Al-Bab for weeks.
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.
It has proved the bloodiest battle of Ankara’s campaign accounting for most of the 69 Turkish losses so far.
Turkish Defence Minister Fikri Isik said on Thursday 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 (one mile) from its outskirts in recent weeks.
On Thursday afternoon, an AFP correspondent heard intermittent gunfire as rebel units continued to clear the heavily damaged town.
Rebels pounded outside Aleppo
The battle against IS around Al-Bab is just one front line in the fighting 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.
Exchanges of rocket and artillery fire first broke out on Wednesday, centred on the rebel-held district of Rashideen, the Observatory said.
The government responded with intensive air strikes on Thursday that killed at least 32 rebel fighters.
“The regime wants to reinforce its positions around Aleppo and is using the rocket fire by the rebels as a pretext to bombard their positions and attempt to drive them out of the suburbs,” Observatory chief Rami Abdel Rahman told AFP.
A fragile ceasefire between government forces and non-jihadist rebels has been in force since late December, brokered by regime ally Russia and rebel backer Turkey.
It has led to a sharp reduction in fighting in many areas.
But parts of the country which are held by IS or its jihadist rival, former Al-Qaeda affiliate Fateh al-Sham Front, are not covered by the truce.
The talks in Geneva between government and opposition representatives formally opened on Thursday.
They are the fourth round of UN-brokered negotiations, aimed at ending a conflict that has dragged on for nearly six years and claimed more than 310,000 lives.
UN envoy Staffan de Mistura said: “I’m not expecting miracles,” but warned of dire consequences if the talks “fail again”.