A spokeswoman for the US navy's Bahrain-based Fifth Fleet said five other occupation personnel were also wounded in the blasts that appeared to be coordinated human-bomb attacks.
A British Defence Ministry spokeswoman said the attacks on Saturday evening failed to damage the oil terminal.
Two of the attacking boats exploded alongside a ship anchored at the terminal about 10km offshore.
The third boat was intercepted as it approached an exclusion zone around the terminal and there was an explosion soon after occupation personnel boarded it to check.
Officials at Iraq's Southern Oil Company said the Basra terminal had been shut down.
"All workers were evacuated from the Basra teriminal. We are concerned about the possibility of more attacks," an official said.
It was the first known maritime attack on Iraqi oil facilities since the March 2003 US-led invasion of Iraq.
Resistance fighters have been attacking pipelines in the north and south of Iraq, at times disrupting the export of oil.
The attack appeared to resemble a 12 October 2000 attack on the USS Cole off Yemen, in which an explosives-laden boat rammed the destroyer, killing 17 American sailors.
Also, on 6 October 2002, a boat rammed a French oil tanker off the coast of Yemen and exploded, killing one crewman.
Both those attacks were blamed on al-Qaida.
The oil attacks came three days after near simultaneous car bombings in the southern Iraqi city of Basra, 50km from Umm Qasr, that killed 74 people.