The deaths take the national toll to at least 15 after the United Nations said that seven other people were killed by flooding in the north, where the country's long conflict is raging between the government and the Iran-backed Houthi rebels.
A government official told AFP that along with the deaths in southern city Aden, at least 10 homes were destroyed and 90 others severely damaged.
The flooding compounds the country's troubles, as it struggles to fend off water-borne diseases like cholera and also braces for the spread of the novel coronavirus, after recording one case so far.
Oxfam said on Wednesday that it was "extremely worried" about the recent storms, which have also hit other provinces across the country.
"People have died, houses damaged, [camps for displaced people] have been affected and this flooding may accelerate the spread of cholera," Samah Hadid, director of advocacy for Oxfam Yemen, told AFP.
More than three million people are displaced in Yemen, which has been ravaged by years of war, with many in camps that are especially vulnerable to disease.
"Oxfam is projecting that there could be one million cases of cholera this year with the start of the rainy season in Yemen," Hadid said.
"This is occurring in addition to the serious threat of coronavirus in the country."
At least 35 families were stuck in their homes on Wednesday, their houses submerged in water and mud, residents in Aden told AFP.
Hundreds of vehicles were stranded in the middle of flooded streets, and in one part of the city, a boy sat in a styrofoam box and used a plank to row across the thoroughfare.
Mohammed Abdulhakim, an Aden resident, said the situation in the city was dire.
"There is water and mud in my home, cars have been swept along the roads, which are now completely blocked and destroyed," he told AFP.
Families lose everything
The UN refugee agency said Wednesday that the heavy rains and flooding have affected displaced Yemenis across the country, including the rebel-held capital Sanaa and the flashpoint northern province of Marib.
"Many families lost their shelter, and everything they own," the UNHCR said in a Twitter post accompanied by an image of a man transporting two children across the flooded streets in a tub.
The UN said on Tuesday that at least seven people have been killed and 85 injured in flash flooding in the northern governorates of Yemen this month.
The same day, Yemen's Prime Minister Moeen Abdulmalik Saeed declared Aden, where the government has been based after the rebels seized Sanaa, a "disaster zone".
An estimated 24 million Yemenis -- more than 80 per cent of the population -- depend on some form of humanitarian aid or protection for survival, according to the UN.