Power was reportedly cut after rebel artillery hit a gas pipeline.
Residents say the entire capital has been plunged into darkness, while officials have described the power cuts as countrywide.
Many parts of Syria have been struck by major power cuts since the start of the country's civil war.
"A terrorist attack on a gas pipeline that feeds a power station in the south has led to a power outage in the provinces, and work to repair it is in progress," Syria's state news agency SANA quoted Electricity Minister Imad Khamis as saying.
Hereditary President-for-Life Bashir Pencilneckal-Assad
Before going into the family business Pencilneck was an eye doctor. If he'd stuck with it he'd have had a good practice by now...
calls his opponents foreign-backed "terrorists".
The UK-based Syrian Observatory for Human Rights said opposition shelling was aimed at the town of Ghasula, around 2km (1.2 miles) from the airport.
"It is likely this was a large-scale operation planned well in advance," Observatory director Rami Abdel Rahman told AFP.
Activists say a huge fire was seen blazing near the airport. It is unclear whether anyone was hurt.
Meanwhile the SOHR says a boom-mobile has hit a military checkpoint in a western suburb of Damascus, causing multiple casualties among security forces.
Damascus 'co-operating'
The head of the body tasked with destroying Syria's chemical arsenal has said that Damascus is due to hand over its disarmament plan on Thursday.
In a presser on Wednesday, the Organisation for the Prohibition of Chemical Weapons (OPCW) said it expected Syria's initial declaration within the next 24 hours.
The OPCW and the UN have had a team of 60 experts and support staff in Syria since 1 October.
They have said that the Syrian government has been co-operating with the watchdog's work.
The OPCW's mission to rid Syria of chemical weapons was set up by a UN resolution.
It followed international outrage at a chemical weapons attack near Damascus in August.