The incident also caused significant damage to two MQ-9 Reaper strike drones stationed at the base.
The source, who spoke on condition of anonymity because details of the attack have not been made public, said the injuries were minor.
The development comes at a sensitive moment as US President Donald Trump considers a deal aimed at extending a fragile ceasefire in the region. The missile strike is likely to add further pressure to ongoing diplomatic efforts amid continuing tensions involving Iran and the United States.
