The Syrian Observatory for Human Rights said seven women were among those killed in raids using explosive barrel bombs on the town in northern Aleppo province.
One of the places hit in Al-Bab was a market selling petrol, the Britain-based monitor said.
More than 40 people were wounded and 10 others were still missing after the raids.
The Local Coordination Committees activist network said charred bodies were recovered from the site of one of the strikes.
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Syria's army has regularly targeted Al-Bab, which has been held by IS since early 2014, but the town has also been hit on occasion by US-led air strikes.
The Syrian government forces have been repeatedly accused of indiscriminantly using barrel bombs on civilian areas. The regime denies deploying the weapons.
The bombs are crudely constructed from weapons fashioned from barrels and other vessels such as gas cylinders packed with explosives and scraps of metal.
But the bombs used by the army on Saturday and Monday were reportedly even larger than the regular barrel bombs.