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. READ MORE