At least seven women and four children were among those killed, they said.
As many as 362,545 suspected cholera cases and 1,817 related deaths have been reported in 91.3 per cent of Yemeni governorates and 88 percent of its districts, said a World Health Organization report on July 19.
The war in Yemen shows no signs of stopping, with the Saudi-led coalition continuing its military campaign.
The UN agency said the capital Sanaa was among the provinces hardest-hit by the disease, while the highest number of deaths was recorded in the northwestern Hajjah province.
Earlier, the officials said the family was fleeing from the fighting raging in the province.
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Since March 2015, Saudi Arabia and some of its Arab allies have been carrying out deadly airstrikes against the Houthi Ansarullah movement in an attempt to restore power to the fugitive former president Abd Rabbuh Mansour Hadi, a close ally of Riyadh. However, they "continue to be exposed to danger as the conflict has affected all of Yemen's mainland governorates", UNHCR said in its statement Tuesday.
Last month, an air raid on a market in rebel-controlled Saada province, in north Yemen, killed 24 civilians.
According to Save the Children, over 4,000 children have been killed or injured as a direct outcome of the conflict, while half a million children are estimated at risk of dying from malnutrition. "UNHCR, as the lead agency for protection under the coordinated humanitarian response in Yemen, has been appealing to parties to the conflict to ensure their utmost in the protection of civilians and the mitigation of suffering".
The coalition has since March 2015 been targeting Houthi rebels fighting pro-government forces in Yemen in the country's deadly civil war and worldwide rights groups accuse it of bombing civilian gatherings, markets, hospitals and residential areas across the country.
Campaigners in the West have urged countries including the United States and Britain to suspend arms exports to Saudi Arabia over civilian casualties in the conflict.