State news agency SANA said the vehicle targeted the Arman neighborhood, home to mostly minority Christians and Alawites, the sect of the President Bashar Assad. It said two rockets also were fired at the site after the bombing.
The British-based Syrian Observatory for Human Rights also reported the bombing and death toll.
The Arman neighbourhood has been repeatedly hit by car bombs. Syria's conflict, which began as a 2011 uprising, has turned into a chaotic war with sectarian overtones.