Riyadh has repeatedly accused the Houthis of acting as a proxy force for Shia Iran, Saudi Arabia's arch-foe in the region.
One of the Saudi oil tankers was attacked west of Hodeidah, a port now under Houthi control, Turki al-Maliki, spokesman for the Saudi-led Arab coalition told Al Arabiya.
The coalition spokesman described it as a "terrorist attack" that threatens commercial shipping routes in the vital Bab al-Mandeb strait, used for oil shipments from the Gulf to Europe, as well as goods from Asia to Europe.
The coalition said a naval ship belonging to a member country rapidly intervened, without giving further details.
However, humanitarian officials said the Houthi-held port of Hudaydah, a major lifeline for the war-torn impoverished country, remains "a wasteland", noting that a "de facto blockade" on the main port is still in place.
Several children were among those killed in a strike on the rebel-held Yemeni port of Hodeida on Monday (April 2), the United Nations said, calling it "one of the deadliest attacks" on minors in the country for years.
In November 2017, Saudi Arabia announced that it was shutting down Yemen's air, sea, and land borders.
The Houthis, in turn, have launched rockets into Saudi territory with mixed results.
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Earlier on Tuesday, U.N. Secretary-General Antonio Guterres urged the warring sides in Yemen to reach a political settlement to end a conflict now in its fourth year that has left 22 million people in urgent need of aid.
The UN's Yemen envoy, Martin Griffiths, has recently visited Riyadh and Sanaa in hopes of revitalising sputtering peace talks.
Guterres said he saw "positive perspectives" for preparing a plan of action "to lead to an effective inter-Yemeni dialogue able to achieve a political solution, with of course the involvement of all those that are relevant in this conflict".
The Houthi militias have stepped up their attacks on Saudi targets by firing missiles at the kingdom in retaliation for the Saudi-led Arab coalition's airstrikes in Yemen.
"The Houthis should immediately stop their indiscriminate missile attacks on populated areas of Saudi Arabia", said Sarah Leah Whitson, Middle East director at Human Rights Watch.
Last year's Yemen appeal was for $2.5 billion, which was 73 percent funded, but the needs have intensified since.
Meanwhile, Yemen's foreign minister, who was also present at the conference, called for a return to the negotiating table to end the devastating three-year civil war in the country.