Elsewhere, Riyadh said four Saudi security personnel were killed in cross-border rocket fire and shelling, while Yemeni sources said nine rebels were killed in clashes with pro-government forces in Dhaleh province.
The suicide bombing took place near the city of Qoton in southeastern Yemen's vast desert province of Hadramawt, where Al-Qaeda in the Arabian Peninsula (AQAP) operates.
The source said the dead soldiers were members of the army's First Division, loyal to exiled President Abedrabbo Mansour Hadi.
Separately, the source said AQAP militants flogged eight people in the Hadramawt provincial capital of Mukalla, a port city of more than 200,000 people that they control.
Charged with offences including adultery and drug and alcohol use, the eight received between 80 and 100 lashes each in a punishment carried out in a public square before hundreds of witnesses.
In March, a Saudi-led coalition launched an air campaign against the Huthis and allied forces loyal to former president Ali Abdullah Saleh in a bid to restore the authority of Hadi, who has taken refuge in Riyadh.
The Saudi interior ministry, meanwhile, said cross-border rocket fire and shelling killed three soldiers and a member of a paramilitary force in the Asir and Jazan regions.
The bombardment came during a day of relative calm in Yemen itself.
Government-aligned forces have since last week been expanding their area of control after recapturing the southern port city of Aden.
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