The floods in Al-Mahwit, a province west of the capital Sanaa controlled by Iran-backed Huthi rebels, triggered landslides that swept through several homes, police said in a statement carried by rebel media.
At least 24 people are missing after seven homes were destroyed in the province's Melhan district, police said.
Authorities have yet to report casualties but images circulating on social media purported to show corpses wrapped in blankets after the floods.
AFP could not independently verify their authenticity.
The mountains of western Yemen are prone to heavy seasonal rainfall. Since late July, flash flooding has killed 60 people and affected 268,000, according to the United Nations.
Western and central provinces have been warned of worse to come.
"In the coming months, increased rainfall is forecast, with the central highlands, Red Sea coastal areas and portions of the southern uplands expected to receive unprecedented levels in excess of 300 millimetres (12 inches)," the World Health Organization warned on Monday.
Earlier this month, the United Nations warned that $4.9 million was urgently needed to scale up the emergency response to extreme weather in war-torn Yemen.
Climate change is increasing the frequency and intensity of seasonal rains in the Yemeni highlands, much of which are controlled by the Huthi rebels.
A decade of war with the internationally recognised government propped up by a Saudi-led coalition has ravaged medical infrastructure and left millions dependent on international aid.
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