Thick clouds of black smoke could be seen rising over the city after the explosion, in footages aired on TV.
Syria's state news agency Sana said the explosion left three people injured and about 20 cars damaged.
State TV said the blast took place in the parking lot of the Palace of Justice, a compound that houses several courts.
The Local Coordination Committees of Syria confirmed the blast and said it took place in the Marja neighbourhood of central Damascus.
The report blamed armed terrorists groups for the attack.
Syria has been targeted by a series of explosions in recent months, killing dozens of people.
Most of them have targeted the Syrian regime's security agencies.
In May an explosion targeting a military compound in the south of the capital killed 55 people.
The latest blast came a day after seven people died in an attack on the headquarters of a pro-government Syrian TV channel in Damascus just a few miles from the presidential palace. Gunmen raided the building and set off explosives inside.