Speaking from Gaza, Hamas spokesperson Mushir al-Masri said his group was convinced Israel was behind the attack and was investigating the incident which took place on Monday.
"This is the second incident in which an explosion targets a Hamas member," a Palestinian source said.
He said the bomb, placed under the driver's seat, blew up shortly after the unnamed member and his daughter had parked the car and left it. The Hamas member and his daughter were unhurt.
Israel has denied any complicity in the incident.
Earlier, 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.
"The party behind this collaborates with the Israeli Mossad, or is the Mossad itself," Ghazi Kanaan said on Syrian television. His comments were carried by Syria's official SANA news agency.
Syrian Information Minister Mahdi Dakhl Allah also said the bombing of a car belonging to a member of the Palestinian movement Hamas in Damascus showed Israel continued to reject peace.
The blast on Monday "is part of the Israeli terrorist war led against Palestinian civilians wherever they be", the minister said.
"It's a new signal showing that peace does not figure on Israel's agenda," the minister said, adding that Israel was not ready for peace because of its continued policy of "terrorism" against the Arabs.
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.
A Hamas official, Izz al-Din Subhi Shaikh Khalil, 42, was killed when a bomb ripped through his car in Damascus on 26 September.