The Black Hawk helicopter crashed in the eastern province of Marib, the coalition said, adding that it is investigating the circumstances.
The incident happened as US Defence Secretary James Mattis arrived in the Saudi capital to discuss the Yemen war with Saudi leaders.
The coalition of mostly Arab Sunni countries has waged a campaign to dislodge Yemeni Shiite rebels, known as Houthis, who seized Yemen's capital and some other areas in 2014 and forced the internationally-recognised government to flee the country.
The single deadliest incident for coalition forces killed 45 troops from the United Arab Emirates in September 2015, when a rebel missile hit a weapons depot also in Marib.
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It was the deadliest day for its military in the UAE's 44-year history. Ten Saudis were killed in the blast too. Bahrain also lost five soldiers, though it was not clear if they were killed in the same incident.
He said the Trump administration's goal is for the crisis "to be put in front of a UN-brokered negotiating team and try to resolve this politically as soon as possible."
He also echoed past Saudi accusations that Houthis have been receiving arms from Iran, saying that the Iranians have supplied Houthis with missiles they use to fire on Saudi Arabia.
Mattis is the highest-level Trump administration official to visit the kingdom. Deputy Crown Prince Mohammed bin Salman, who is also Saudi defence minister, met Trump at the White House last month.
President Abed-Rabbo Mansour Hadi insists on the implementation of the UN Security Council resolutions which stipulate that the Houthis pull their militias from the cities and hand over heavy weapons, while the Shiite rebels demand on a power-sharing deal before taking any security-related steps.
Hadi's government, backed by the Saudi-led coalition, has regained control over southern Yemen, but has however failed to restore law and order in that part of the country as the extremist Islamic State group and al-Qaida militants have grown in numbers and expanded their footprints.