Prince Harry, third in line to the British throne, is stationed at the base on a four-month combat tour. There was no immediate word on his whereabouts at the time of the attack.
U.S. officials said the attack at Camp Bastion in Afghanistan's Helmand province involved a range of insurgent weaponry, possibly including mortars, rockets or rocket-propelled grenades, as well as small arms fire.
The official spoke on condition of anonymity because U.S. military authorities in Afghanistan had not yet announced the battle.
Camp Bastion is a British air base and is adjacent to Camp Leatherneck, the main base for U.S. Marines in Helmand.
A number of aircraft at the base also were hit by insurgent fire, the official said.
Capt. Harry Wales, as the prince is known in the military, is serving a four-month combat deployment as a gunner on an Apache helicopter. Harry, who turns 28 on Saturday, is expected to start flying Apache missions this week. This is his second tour in Afghanistan.
It also was not clear Friday whether the attack was linked at all to the protests and violence across the Muslim world this week that has been linked to an anti-Islamic film. Afghanistan's southern region has been a hotbed of the insurgency and frequent attacks.