Yemen's Iran-aligned Houthi group has been launching drone and missile strikes in shipping lanes since November, saying that it acts in solidarity with Palestinians in Israel's war in Gaza.
In dozens of attacks, the Houthis have sunk two vessels, seized another and killed at least three seafarers.
A Houthi statement said the Transworld Navigator took a direct hit from a missile. The operation against the Eisenhower had achieved its objectives successfully, it said, without elaborating.
The Houthi attacks are continuing, and severe damage is being inflicted on global trade, with no end in sight.
The ship was struck by missiles and an explosive-laden remote-controlled boat on June 12 and had been taking on water. One crew member remains missing.
According to a statement from the State Department, Monday's sanctions include three individuals and six entities that facilitated weapons procurement for the Houthis.
The international community which should have prevented Hamas from controlling Gaza in the first place, has looked on as Iran then set in motion wars across the Middle East.