A fire on board the Chem Pluto was extinguished. There were no casualties.
Iran has not commented. Houthi rebels in Yemen - who are backed by Iran and support Hamas in its war with Israel - have recently used drones and rockets to target vessels in the Red Sea. But this event is the first of its kind so far away from there, according to maritime security firm Ambrey.
The same company also said the vessel was heading from Saudi Arabia to India, and was linked to Israel. The Houthis have claimed to be targeting Israel-linked vessels over the conflict in Gaza.
The US said the Chem Pluto was hit by "a one-way attack drone fired from Iran". It is believed to be the first time the US has publicly accused Iran of targeting a ship directly.
It has previously accused Iran of being "deeply involved" in planning operations against commercial vessels in the Red Sea - a charge Tehran has denied.
However, Iran's Revolutionary Guards have warned they could force the closure of waterways other than the Red Sea if "America and its allies continue committing crimes" in Gaza.
The Pentagon statement said:
"The Chem Pluto, a Liberia-flagged, Japanese-owned, and Netherlands-operated chemical tanker, was struck on Saturday at 10:00 local time (06:00 GMT). The hit caused structural damage.Ambrey said the event fell within an area considered a 'heightened threat area' for Iranian drones.
"The incident took place 200 nautical miles (370km) south-west of the city of Veraval in India's Gujarat state, according to United Kingdom Maritime Trade Operations (UKMTO)."
The Indian navy sent an aircraft and warships to offer assistance. The BBC was not able to independently verify the incident.
In a separate development, the US Central Command (Centcom) said:
"On Saturday two Houthi anti-ship ballistic missiles were fired into international shipping lanes in the Southern Red Sea from Houthi-controlled areas of Yemen. No ships reported being impacted.Later that day, a crude oil tanker reported being hit by a Houthi drone in the southern Red Sea, while another tanker saw a near miss.
"The USS Laboon warship patrolling the area shot down four unmanned aerial drones originating from Houthi-controlled areas in Yemen that were inbound to the American vessel."
Many global shipping groups have suspended operations in the Red Sea due to the increased risk of attacks. The UK government has vowed to ensure the route's safety.
Defence Secretary Grant Shapps told the Sunday Times newspaper that the UK was committed to repelling attacks on vessels - and would not allow the Red Sea to become a 'no-go area'.
Meanwhile, Foreign Secretary David Cameron described Iran as:
"A thoroughly malign influence in the region and in the world. The Iranian leadership and its proxies need to be sent an 'incredibly clear message' that this escalation will not be tolerated."
Comment: A trigger attempt? It must drive certain countries nuts that Iran chooses wisely what it says and does.
Chris Farrell from Neptune P2P Group, a UK maritime security company, described nervousness in the region and observed that container ships were proving more likely to reroute than larger vessels.
He told the BBC World Service's Weekend programme:
"Nobody really knows the situation out there because of the lack of stability. That's creating the uncertainty with the clients and the shipping companies which are putting their assets within that region."




The stage is being set. Expect a false flag spectacular soon. Houthi = Iran or so we are being led to believe. Middle East conflagration any day now. Just in time for the holiday season when the masses have more time to watch rolling news coverage.
Merry Christmas.