The attack targeted a sports and culture club in the Huthi-controlled town of Radaa, he said, in the central province of Baida where Al-Qaeda fighters are present.
A security official said: "Huthi fighters opened fire on the car before it attacked the club, causing it to explode at the gate, leading to the deaths and injuries."
A nearby school was also damaged, the source said.
Late last month, dozens of suspected Al-Qaeda militants, civilians and a US Navy Seal were killed in a US raid on a compound in the same province.
AQAP and the Islamic State jihadist group have exploited a power vacuum created by the conflict between the government and the Shiite rebels to expand their presence in Yemen.
More than 7,400 people have been killed in the war since a Saudi-led coalition started a military intervention in support of the government in March 2015, the UN says.
That toll includes around 1,400 children.
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