"Initial reports indicate that some 3,730 families [22,380 people] have been affected by the rains and flooding, the majority of whom are internally displaced people," the UN humanitarian agency Office for Coordination of Humanitarian Affairs [OCHA] said.
"Intensified rainfall over the past few days is causing damage to infrastructure, destroying homes and shelter and causing deaths and injuries."
On Monday, the government said four people were killed in flash floods in the historic city of Tarim in the central province of Hadramawt, and the UN cited reports of three deaths elsewhere in the country.
AFP footage showed city streets in Tarim flooded and its famed mud-brick buildings in ruins, with cars and motorcycles buried under mud and debris.
The UN office said flooding also caused extensive damage in the provinces of Aden, Abyan, Daleh, Lahj, Hadramawt, Marib and Taiz.
Dozens of people are killed every year across Yemen due to flash floods.
Fierce storms have added to the woes of the conflict-ridden country.
Yemen is suffering the world's worst humanitarian crisis as a years-long war rumbles on, with over four million people displaced and two-thirds of its 30-million population dependent on aid.
Tens of thousands of people have been killed and millions pushed to the brink of famine over the course of seven years of war on Yemen.