"Airlines are not operating to Damascus today as the airport was not accepting any flights," said the Dubai-based airline official, who declined to be identified.
Flight schedules on aviation websites showed that two airlines based in the Gulf - Air Arabia and flydubai - would normally operate flights to Damascus on a Friday.
Syria's information ministry said on Thursday the airport road was safe after security forces cleared it of "terrorists" - the label Damascus uses to describe rebels fighting to overthrow Bashar al-Assad - and the airport was operating normally.
The 20-month-old conflict in Syria has already led several airlines to cancel or cut back flights to Damascus, and only a handful of commercial flights a day land and take off from the airport, according to flight timetables.
Rami Abdelrahman, director of the British-based Syrian Observatory for Human Rights, said the airport road had been re-opened but Assad's forces and rebels were still fighting nearby and traffic on the highway was minimal.
He said there were reports of clashes and artillery bombardment continuing through the night in southern Damascus, but contact with sources inside the country was difficult because the Internet and most telephone lines were still down.