Both Syrian state television and the opposition Syrian Observatory for Human Rights reported the incident.
One person was killed in the car bombing, the observatory said.
No one immediately claimed responsibility for the blast.
Mezzeh, the neighborhood in southwest Damascus, is a strategically important because it is located along the Mezzeh highway that connects to a major Syrian air force base.
It is also near Mount Mezzeh, where President Bashar al-Assad’s palace is located.
For months, Syrian rebels have been trying to infiltrate Damascus in their attempt to oust al-Assad and end four decades of family rule.
The civil war in Syria has killed more than 70,000 people, mostly civilians, over the past two years.