The TV report quoted an unnamed military official as saying that the helicopter crashed today as a result of a technical problem while taking off.
The report did not say how many crew members were on abroad at the time of the crash.
The Britain-based Syrian Observatory for Human Rights said Islamic State militants who have been laying siege to the base for months shot down the helicopter. The Observatory said one crew member was killed while the fate of the others remained unclear.
Syrian rebels have shot down helicopters in the past.