The victims of the bombing, which hit Al Atera village in Taiz province, were internally displaced people and are believed to be from the same family, the UN says.
An air strike by the Saudi-led coalition battling Yemeni rebels struck a vehicle packed with fleeing people on Tuesday, killing at least 20, Yemeni security officials and officials from the armed Houthi movement said on Wednesday.
The UN said that the victims of the bombing, which hit Al Atera village in Taiz province where fighting between Yemen's two warring sides has intensified, were internally displaced people (or IDPs).
Yemen's human rights minister, Mohammed Askar, called for a government investigation into what he described as an "unfortunate incident" while Houthi spokesman Mohammed Abdul-Salam condemned it as a "monstrous crime."
Shabia Mantoo, United Nations High Commissioner for Refugees (UNHCR) spokesperson in Yemen, said that most of those killed were believed to be from the same family.
Earlier Yemen's security officials said that the people were struck while they were fleeing.
International rights groups have accused the coalition of bombing civilian gatherings, markets, hospitals, and residential areas across Yemen since the beginning of its campaign against Houthi rebels in 2015.
UN flight to Sanaa barred
Separately, the United Nations officials said that the coalition barred a UN flight to Yemen's capital, Sanaa, which is controlled by the Houthis.
The plane was going to bring aid workers and reporters from Djibouti. The coalition shut down Sanaa's international airport a year ago.
"The coalition claimed that the security of the journalists could not be guaranteed in rebel-controlled areas and advised the three journalists to travel on commercial flights," said Ahmed Ben Lassoued, a spokesman for the United Nations Office for the Coordination of Humanitarian Affairs (OCHA) in Yemen.
Deadlocked war and cholera
The war has been mired in a stalemate for most of the last two years, with more than 10,000 people killed and three million displaced.
The fighting has pushed the Arab world's poorest country to the brink of famine, and a cholera outbreak in recent months has killed more than 1,700 people.
With over 332,000 people infected, the disease could spread during the annual Haj pilgrimage to Mecca, WHO has warned.