The coalition yesterday said three Huthi rebel boats attacked a Saudi frigate on patrol west of Hodeida, a Yemeni coastal city held by the insurgents.
It did not say when the incident occurred.
Although the Saudi warship "dealt with the boats," one of them "collided with the back of the ship and exploded and caused a fire" which the crew brought under control.
As a result of the incident two Saudi crewmen lost their lives and three were wounded, the coalition said, adding the frigate was able to resume its patrol.
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Riyadh accuses Iran of arming the Huthis, a charge Tehran denies.
The coalition intervened after the rebels and their allies overran the capital Sanaa and moved on to other parts of Yemen, forcing President Abedrabbo Mansour Hadi to flee to Riyadh where he still spends most of his time.
United Nations mediation and seven ceasefires have failed to stop the fighting, which the UN warned has left Yemen at risk of famine this year.
That process would occur in tandem with a Huthi withdrawal from the capital and other cities.
Hadi refuses to discuss the proposals, the envoy told the UN Security Council last week.