The Syrian interior ministry accused Israel's secret service Mossad of being behind the attack on what it originally said was a member of the Hamas movement.
"This is the second incident in which an explosion targets a Hamas member," the source said.
He said the bomb, placed under the driver's seat, blew up shortly after the unnamed member had parked the car and left it.
"The party behind this collaborates with the Israeli Mossad, or is the Mossad itself," Ghazi Kanaan said on Syrian television, referring to the Israeli intelligence agency. His comments were carried by Syria's official SANA news agency.
"The Palestinian, a dentist, and his wife parked the car and got off. The car exploded five minutes shortly after they left it", the minister said
Musa Abu Marzuk, Hamas' deputy political bureau leader, said the vehicle belonged to a Palestinian member of Hamas. He would not give his name or position in the movement.
Several Hamas officials are resident in Damascus, the most prominent of whom is Khalid Mishaal, the head of Hamas' political wing. He survived a botched Israeli assassination attempt in Jordan in 1997.
The silver sports utility vehicle was quickly removed by security and rescue teams who were collecting shrapnel scattered on the street in the Mazza area of the city, they said.
"The explosion was so strong that the door blew open in my house, and windows were shattered in the whole building," resident Isam Abd al-Wahid said.
Three passersby were injured in the blast and nearby buildings had their windows blown out.
The blast occurred near a hospital and a petrol station which was not damaged.
Syrians stand outside a building
damaged by the blast
It followed an audacious resistance attack in Gaza overnight, claimed jointly by Hamas and the Fatah Hawks, in which five Israeli occupation soldiers were killed and up to 13 injured.
Israel has been accused of targeting Palestinian resistance targets based in Syria in recent months. A Hamas official was killed when a bomb ripped through his car in Damascus on 26 September.
The explosion, blamed on Israel, killed Izz al-Din Subhi Shaikh Khalil, 42, and wounded three bystanders.
Syrian authorities and Hamas blamed Israel for that attack.
In 2003, Israeli jets bombed what the country said was a training camp used by a Palestinian group in Syria.