The attack occurred off Yanbu in the Red Sea and comes as the rebels continue their declared naval blockade of Saudi Arabia.
It is the eighth Saudi oil tanker to be attacked since the blockade began on July 22, said military spokesman Yahya Saree.
They "managed to hit the Saudi oil tanker 'Wafa' with a number of ballistic missiles," he said.
The move threatens an escalation of attacks.
After the Iran war closed the Strait of Hormuz out of the Persian Gulf, Yanbu on the Red Sea on the other side of the Arabian Peninsula has become the main export port for Saudi oil.
