Ambrey said a radio communication indicated the vessel was hit by a missile and that there was a fire onboard.
In March, the group's leader said the group was expanding its attack area to prevent Israel-linked ships from passing through the Indian Ocean toward the Cape of Good Hope.
The tanker, which was not identified by name, was en route from Pimorsk, Russia, to Vadinar, India, when it was attacked, Ambrey said in its advisory note.
Last week the Houthis's leader warned that the group would begin attacking ships heading toward the Cape of Good Hope in Africa's southern tip.
More thought needs to be put into what to do when and if ships are struck by missiles. Letting ships slowly sink is not a good solution.
Yemen's Houthis said on Tuesday they could only reconsider their missile and drone attacks on international shipping in the Red Sea once Israel ends its "aggression" in the Gaza Strip.
The ship was heading north during its journey from Khor Fakkan in the United Arab Emirates to Varna, Bulgaria, when the attack occurred, Ambrey said in an advisory note.
The US State Department said on Friday that the vessel, which was carrying crude oil bound for India, was hit by a missile on its port side.
In 2022, the EU designated the Northwest Indian Ocean a “maritime area of interest,” an area spanning from the Strait of Hormuz to the Tropic of Capricorn, and from the Red Sea to the Indian Ocean.
Seafarers remain in the firing line, and have already signed agreements to receive double pay when entering the high-risk zones.