The man blew himself up inside the vehicle yesterday on a busy road on the outskirts of the city in central Syria, the state news agency said. It blamed "terrorists", the term it uses to describe rebel forces trying to topple President Bashar al-Assad.
The pro-opposition Syrian Observatory for Human Rights said the attack targeted an army checkpoint but most of the dead were civilians.
Syria's two-and-a-half year conflict began as peaceful protests but has turned into civil war. More than 100,000 people have died, according to UN figures, in fighting that has spread across most of the country.
Rebels have been joined by hardline Islamists, some of them linked to al Qaeda, who have become increasingly powerful among opposition forces.
According to the London-based Observatory, the suicide bomber in yesterday's attack from the Nusra Front, an al Qaeda affiliate that has frequently used suicide bombers to attack military and political targets.
Pictures on Syria TV showed firemen trying to put out huge fires as black smoke rose from charred trucks and cars.
Rebels also used a car bomb a day earlier to attack a checkpoint on the outskirts of Damascus. Heavy clashes erupted after the blast and continued yesterday.
Rebels said they seized the first checkpoint and were now fighting to capture a second one further down the road. The checkpoints, to the south-east of the capital, sit between the rebel-held suburb of Mleiha and the government-held suburb of Jaramana.
"These checkpoints are the fortress between us and the next air force defence site," said Nidal, a rebel speaking by Skype. "If we can destroy it we can liberate the base."
Syrian military jets have pounded nearby rebel-held areas. Rebels hold several suburbs ringing the capital but have yet to make deep inroads into the capital due to a sustained army blockade.
Doctors in one suburb to the west of Damascus, Mouadamiya, have reported an increasing number of deaths due to malnutrition.
A fighter in the eastern suburbs said government forces had blocked the main entry point for food and supplies to that region two days ago.
"That is where we used to get our food and flour. If it stays closed, we will be destroyed," he said, asking not to be named.
International powers are trying to bring the two sides to peace talks in Geneva next month but the opposition has been reluctant to attend and Mr Assad's government says it will not negotiate the president's removal.
Arab League chief Nabil Elaraby said yesterday that talks aimed at ending the civil war in Syria were scheduled for November 23, but Lakhdar Brahimi, the international envoy for Syria, said no date had yet been set.
Speaking in Cairo, Mr Brahimi said he would travel to Qatar, Turkey, Iran and Syria, as well as Geneva, to meet American, Russian and Security Council member officials "after which a final date for the Geneva 2 conference will be announced".
Iran is Mr Assad's most important regional backer and the prospect of a peace conference raises questions over whether it will be invited, something Washington has resisted unless Tehran states publicly it would support a transition government in Syria. That would mean Mr Assad should step down.
Also unclear is who, if anyone, would attend from Syria's divided opposition.
Najib Ghadbian, the opposition coalition's US representative, said an important part of the coalition had decided against taking part, but other members of the umbrella group could still decide to go, assuming Mr Assad was not there.
Mr Assad's government has said it would not consider any deal that required the president to step down.
Meanwhile, a Friends of Syria meeting is due to take place in London tomorrow.