Dozens of other combatants were wounded in the gunfight that erupted on the western outskirts of Amran city, the medics at Amran hospital said.
A military source said earlier that three soldiers were killed in the clashes which broke out when rebels attacked an army position in the area.
Tensions remain high in Amran where Huthis have been trying to enforce their presence through armed parades and protests against the military.
But the suspected aim of the rebels is to enlarge their sphere of influence as the country is set to be split into six regions, pushing out from their mountain strongholds in the far north to areas closer to the capital Sanaa.
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The Huthis have fought the central government in Sanaa for years, complaining of marginalisation under former president Ali Abdullah Saleh, who was ousted in 2012 following a year of protests.
In February, they seized areas of Amran province in fighting with tribes that left more than 150 people dead.
The rebels, known also as Ansarullah, had to withdraw from some of these areas following a truce with the armed tribes and as the army deployed halting the advance of the rebels towards the capital.
It is also fighting a fierce war against Al-Qaeda in southern and eastern areas.
Al-Qaeda in the Arabian Peninsula, or AQAP, is considered by Washington as the most dangerous affiliate of the jihadist network after being linked to several failed plots against the United States.