Volunteers from the Syrian Civil Defense operating in opposition-held areas said the death toll could rise. He added that a woman was among the dead.
The Syrian Observatory for Human Rights put the death toll at 6, including opposition fighters. He explained that the bodies were badly burned.
The explosion occurred near the market in the city center, not far from a point belonging to the Army of Islam, according to the observatory. The observatory also said 12 people were wounded, including two children.
Turkey and allied Syrian fighters have controlled Afrin since 2018, after an operation that drove out local Kurdish fighters and displaced thousands of Kurdish residents.
Since then, the town has been the site of frequent car bombings, which have gone largely unclaimed.
Turkish officials blamed the attack on the armed Kurdish People’s Protection Units (YPG), and US-backed Kurdish forces denied involvement.