One drone was shot down, but another caused minor injuries, said one of the officials, who spoke on condition of anonymity to discuss the matter before an official announcement about the incident.
The attacks follow similar drone strikes over the past few days against U.S. and coalition bases in Iraq amid simmering anger in the region after a deadly explosion at a Gaza hospital on Oct 17. According to the Hamas-run Ministry of Health, the hospital explosion killed hundreds of people.
The al-Tanf garrison in southeastern Syria is located at a sensitive juncture often used by Iranian-backed militants to ferry weapons to Hezbollah.
Syrian opposition activists also said Thursday a drone attack was conducted on an oil facility in eastern Syria that houses American troops.
Omar Abu Layla, a Europe-based activist who heads the Deir Ezzor 24 media outlet, said three drones with explosives struck the Conoco gas field in the eastern province of Deir el-Zour that borders Iraq.
Rami Abdurrahman of the Britain-based Syrian Observatory for Human Rights, an opposition war monitor, confirmed that five explosions were heard at the Conoco gas field.