The station was packed with people queueing for fuel that has become increasingly scarce during the country's 21-month-long insurgency aimed at overthrowing President Bashar al-Assad.
The semi-official al-Ikhbariya television station showed footage of 10 burnt bodies and Red Crescent workers searching for victims at the site.
The opposition Revolution Leadership Council in Damascus said the explosion was caused by a booby-trapped car.
There was no immediate indication of who was responsible for the bombing in the Barzeh al-Balad district, whose residents include members of the Sunni Muslim majority and other religious and ethnic minorities.
"The station is usually packed even when it has no fuel," said an opposition activist who did not want to be named. "There are lots of people who sleep there overnight, waiting for early morning fuel consignments."
It was the second time that a petrol station has been hit in Damascus this week. Dozens of people were incinerated in an air strike as they waited for fuel on Wednesday, according to opposition sources.
State news agency SANA said the incident was a "terrorist attack" that had targeted a petrol station near a hospital.
The Syrian authorities refer to the anti-Assad rebels as "terrorists" armed and funded from outside the country.
In northern Syria, rebels were battling to seize an air base in their campaign against the air power that Assad has used to bomb rebel-held towns.
More than 60,000 people have been killed in the uprising and civil war, the United Nations said this week, a much higher death toll than previously thought.
After dramatic advances over the second half of 2012, the rebels now hold wide swathes of territory in the north and east, but they cannot protect towns and villages from Assad's helicopters and jets.
Hundreds of rebel fighters were attempting to storm the Taftanaz air base, near the highway that links Syria's two main cities, Aleppo and Damascus.
A rebel fighter speaking from near the Taftanaz base overnight said much of the base was still in loyalist hands but insurgents had managed to destroy a helicopter and a fighter jet on the ground.
The northern rebel Idlib Coordination Committee said the rebels had detonated a car bomb inside the base.
The government's SANA news agency said the base had not fallen and that the military had "strongly confronted an attempt by the terrorists to attack the airport from several axes, inflicting heavy losses among them and destroying their weapons and munitions".
Rami Abdulrahman, head of the opposition-aligned Syrian Observatory for Human Rights which monitors the conflict from Britain, said as many as 800 fighters were involved in the assault, including Islamists from Jabhat al-Nusra, a powerful group that Washington considers terrorists.
Taftanaz is mainly a helicopter base, used for missions to resupply army positions cut off by the rebels, as well as for dropping crude "barrel bombs" on rebel-controlled areas.
Near Minakh, another northern air base that rebels have surrounded, government forces have retaliated by shelling and bombing nearby towns.