Yemen's current monsoon season has been particularly deadly, with some experts saying the war-wrecked country is increasingly vulnerable to severe weather events caused by climate change.
The Al-Masirah TV channel run by the Houthi rebels who control the country's north said the 13 bodies were recovered in Melhan district of Al-Mahwit province. It said a child had been rescued but 20 other people were missing.
Yemen was already the poorest Arab nation before civil war began in 2014, when the Iran-backed Houthis took control of the capital, Sanaa, and much of the north, forcing the government to flee to the south and then to neighboring Saudi Arabia.
Comment: Update August 30
The New Arab reports: Three weeks prior: Flooding in Yemen has left 30 people dead and hundreds displaced, official says