Tearfund says 18.8 million people, nearly three-quarters of the population, urgently need humanitarian assistance.
Saudi Arabia is heading a regional coalition supporting the Yemeni government against Iranian-backed Houthi rebels in the country's civil war.
It is thought Yemen is a few months away from running out of food for its whole population.
Oxfam says the amount of food being imported has been below half the amount needed since August.
Launching its appeal, Tearfund said the civil war had destroyed hospitals and left almost everyone with no access to water.
The charity said it was working to provide basic hygiene and sanitation packs to alleviate the risk of deadly disease and prevent its spread.
Guy Calvert-Lee, Deputy Lead of Eurasia, Latin America and the Caribbean said: ''The situation in Yemen is serious, and has been worsening over some time.
"Massive destruction of medical care facilities, such as hospitals and clinics, has meant there are no hospitals to go to, and millions of people are extremely ill, with recent outbreaks of cholera, dengue and scabies affecting thousands of children.
"Tearfund partners are providing hygiene kits to some of the most vulnerable families to prevent the further spread of disease".
Last weekend, Boris Johnson said the Government was "deeply concerned" about the possible use of UK munitions by the Saudi air force in strikes on civilian targets in the war.
The Foreign Secretary said that the depth of concern in Whitehall about the mounting civilian death toll should not be underestimated.
