The coalition destroyed a boat carrying explosives as it headed toward the tanker on Saturday, coalition spokesman Colonel Turki al-Maliki said.
A coalition statement released later by the official Saudi Press Agency said the warplane that crashed was Saudi and that the operation to rescue the crew involved ground forces.
Tribesmen loyal to the Houthi movement hold their weapons as they attend a gathering to mark 1000 days of the Saudi-led military intervention in the Yemeni conflict, in Sanaa, Yemen December 21, 2017.
The Red Sea is a key shipping route for world trade that connects the Middle East to Europe via the Suez Canal.
The report presented to the UN Security Council on 9 January said: 'The panel has identified missile remnants, related military equipment and military unmanned aerial vehicles (UAVs) that are of Iranian origin and were introduced into Yemen after the imposition of the targeted arms embargo'.More news: China's December imports growth weakest in a year, exports beat forecast
"In a blatant violation of worldwide law, the Iranian-Houthi militia on Saturday attempted an attack by three remote-controlled drone boats, targeting a Saudi oil tanker and threatening to disrupt navigation in Bab El-Mandeb strait", Colonel Turki Al-Maliki.
"If the aggressors keep pushing toward Hodeidah and if the political solution hits wall, there are some strategic choices that will be taken as a no return point, including blocking the worldwide navigation in the Red Sea", Houthis' Ansarullah political council chief, Saleh al-Samad, was quoted saying.
Saudi Arabia and the United States have long accused Iran of arming the Houthis in Yemen, the Arab world's most impoverished country.
The war has killed more than 10,000 Yemenis, mostly civilians, and pushed the country to the brink of mass starvation.