A ballistic missile was fired at the tanker on Wednesday evening, the Houthi movement said. Saudi Arabia has not commented on the incident.
Earlier on Wednesday, a Saudi oil tanker was attacked off Yanbu in the Red Sea, at the same time as the rebels continue their declared naval blockade of Saudi Arabia.
It is the ninth Saudi oil tanker to be attacked since the blockade began on July 22, according to figures provided by the militia.
The movement threatens to escalate its attacks.
After the Iran war caused the closure of the Strait of Hormuz, the Saudi coastal city of Yanbu on the Red Sea, on the other side of the Arabian Peninsula, has become an important export port for Saudi oil.
