The state broadcaster said the bomb was placed in a car in the Rokn Eddin neighbourhood and that a disposal team was sent in to defuse another device.
"The terrorist explosion was the result of a big bomb concealed in a car ... Three people were killed and five others wounded according to a provisional toll," it said.
Television said the blast took place in a car park near a school.
The Syrian Observatory for Human Rights also reported the explosion but gave a higher death toll.
"Several cars were set ablaze and there is property damage in the area," added the Britain-based Observatory which relies on activists and medics on the ground for its reports on Syria's conflict.
On May 1, two bombs in central Damascus killed one person and wounded several others, a day after another bombing killed 13 people in the Syrian capital, according to the Observatory.
State news agency SANA blamed at the time "terrorists" -- the term the regime uses to describe rebels who are fighting to topple President Bashar al-Assad.
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