"The electricity in Damascus has been cut off over an act of sabotage that hit the gas pipeline near the Deir Ali town, resulting in the suspension of operation of the local power station," Zamil told the SANA news agency on late Friday.
The minister later added that electricity was being gradually restored in Damascus.
"Electricity has started to return to Damascus after the launch of Al-Zara, Al Nasryeh and Jandar power stations," the minister said on Saturday, as quoted by SANA.
Pictures reportedly showing the aftermath of the incident have been shared by SANA.
Meanwhile, two transmission lines in the Hauran region have also been targeted, but unsuccessfully, al-Ikhbariya TV reported.
The minister did not state who or what group may have been behind the attack on the gas pipeline.
According to media reports, an explosion was heard in southern Damascus just as the second batch of tankers carrying Iranian fuel was crossing Syria for crisis-hit Lebanon. Hezbollah reportedly arranged the shipments to address a dramatic fuel shortage in the country.
The shipments have been opposed by Western countries, primarily, the US, where Hezbollah was added to the list of terrorist organizations, while any nation that buys Iranian oil is a target for US sanctions.
Hezbollah leader Hassan Nasrallah accused Washington of creating the economic crisis in Lebanon.