The rare shooting not far from approaches to the Strait of Hormuz comes at a period of heightened tensions between the United States and nearby Iran.
A UAE official said the vessel was a fishing boat. It was unclear why it might have veered so close to an armed American vessel.
There was no immediate sign of Iranian involvement, or any indication that the incident was a reprise of al-Qaida's 2000 bombing of the USS Cole in Yemen. But the incident will likely focus further attention on the risks American vessels face in the Gulf even as the Navy beefs up its presence in the region.
Lt. Greg Raelson, a spokesman for the Navy's Bahrain-based 5th Fleet, said a security team aboard the USNS Rappahannock issued a series of warnings before resorting to lethal force about 10 miles (15 kilometers) off the coast of Dubai's Jebel Ali port.
"The U.S. crew repeatedly attempted to warn the vessel's operators to turn away from their deliberate approach. When those efforts failed to deter the approaching vessel, the security team on the Rappahannock fired rounds from a .50-caliber machine gun," he said.
Raelson said the incident, which happened at 2:50 p.m. local time, is under investigation.
The Rappahannock is an oiler used to fuel other Navy ships while they are at sea.
The United Arab Emirates, which includes the commercial hub of Dubai and the oil-rich capital Abu Dhabi, is a key American ally in the Gulf. American warships frequently visit Jebel Ali port, a popular rest stop among U.S. sailors.
A U.S. consular official told The Associated Press that one person was killed and three wounded in the shooting.
The official gave no other details, but it appeared that Navy personnel could have seen the boat - mistakenly or not - as a threat in Gulf waters not far from Iran's maritime boundaries. The official spoke on condition of anonymity because of the sensitivity of the incident between the two allies.
Tariq Ahmed al-Haidan, political affairs assistant to the UAE Foreign Minister, confirmed the number of dead and injured.
He said in a brief statement to the UAE's official news agency WAM that all were Indian citizens, and they were on board a fishing boat when they came under fire. Emirati authorities are investigating the incident, he added.
The white-hulled boat was inspected by dozens of police officers and other Emirati officials after the incident in a small Dubai harbor used by fishermen and recreational sailors.
The boat appeared to be a civilian vessel about 30 feet (9 meters) long and powered by three outboard motors. It had no obvious military markings.
Similar boats are used for fishing in the region, though Iran's Revolutionary Guard also employs relatively small, fast-moving craft in the Gulf.
Rescue workers were seen carrying one person in a body bag off the boat and placing it in an ambulance as fishermen looked on. Officials moved the boat from the harbor shortly afterward.
The U.S. Embassy in Abu Dhabi had no immediate comment, referring all questions to the Navy.
U.S. military vessels routinely cross paths with Iranian ships in international waters in the Gulf without incident, but speed boats from Iran's Revolutionary Guard have passed close to U.S. ships in incidents that have raised alarm in Washington.
In early 2008, then President Bush accused Iran of a "provocative act" after five small Iranian craft buzzed around the destroyer USS Hopper.
Theodore Karasik, a security expert at the Dubai-based Institute for Near East and Gulf Military Analysis, did not rule out Iranian involvement in Monday's shooting.
"There are certain factions within the Iranian political universe who are seeking a fight. And this is one way in which to do it," he said.
Karasik noted there have been no known attacks so close to Jebel Ali, which is seen as a secure port in the region. He suggested that the incident might have been a way for Iranian forces to test U.S. defenses, though he acknowledged it was too early to know for sure.
Tensions are elevated in the Gulf after Iran last week renewed threats to close the strategic Strait of Hormuz - the route for one-fifth of the world's oil - in retaliation for tighter sanctions over Iran's nuclear program.
The U.S. recently boosted its naval presence in the Gulf with additional minesweepers and other warships. The Pentagon said Monday it is sending another aircraft carrier to the Middle East several months early to ensure it has two carriers continuously in the region.
Additional reporting by Associated Press writer Brian Murphy.