The Houthi rebel group attacked a local bazaar while government soldiers were shopping, said a military official who asked not to be named due to restrictions on speaking to the media.
The source said some of the injured are in critical conditions and the death toll might increase.
Houthis’ TV channel Al-Masirah said the attack caused many casualties among government forces.
Impoverished Yemen has remained wracked by violence since 2014, when Shia Houthi rebels overran much of the country, including the capital Sanaa.
The conflict escalated in 2015 when Saudi Arabia and its Sunni-Arab allies launched a devastating air campaign in Yemen aimed at rolling back Houthi gains.
The ongoing violence has destroyed much of Yemen’s infrastructure, including water and sanitation systems, prompting the UN to describe the situation as one of “the worst humanitarian disasters of modern times”.