Iran's Army ground forces public relations office said the "terrorist American army" targeted the facility in Iran's Sistan and Baluchestan province.
The army said passive defence measures and precautionary steps taken had prevented a higher casualty toll, despite the scale and intensity of the strike, which it said was designed to inflict maximum human losses.
Seven personnel were martyred and a number of others were wounded and are receiving treatment.
The army expressed condolences to the families of the "martyred fighters" and to the Iranian nation, and said security along the borders would be maintained.
"The revenge for the pure blood of the martyrs of this crime is certain and imminent," the statement said.
"The Army of the Islamic Republic of Iran, with God's help and alongside other armed forces, will deliver a decisive response to this aggressor action by the American enemy."
MNA