Humanitarian co-ordinator Jamie McGoldrick said the situation was catastrophic and rapidly deteriorating.
Almost 3.3 million people, including 2.1 million children, are suffering from acute malnutrition.
Pro-government forces, supported by a Saudi-led coalition, have been battling the rebel Houthi movement since 2015.
The coalition intervened after the rebels seized the capital, Sanaa, and then forced President Abdrabbuh Mansour Hadi into exile.
Since then, pro-government fighters have driven the rebels out of much of southern Yemen, but the rebels still control Sanaa and large parts of the north-west.
The fighting has left at least 7,470 people dead and 40,000 injured, although the UN says the figure is likely to be higher as it only received reports from the 45% of health facilities that are still functioning.
At the launch of its 2017 humanitarian response plan for Yemen, the UN said two years of war had left an estimated 18.8 million people in need of humanitarian or protection assistance - an increase of almost 20% since late 2014.
An estimated 10.3 million people are acutely affected and need some form of immediate humanitarian assistance to save and sustain their lives, including food, health and medical services, clean water and sanitation, and protection.
"Two years of war have devastated Yemen and millions of children, women and men desperately need our help," Stephen O'Brien, under-secretary-general for humanitarian affairs and emergency relief co-ordinator, said in a statement.
"Without international support, they may face the threat of famine in the course of 2017 and I urge donors to sustain and increase their support to our collective response."
Some 460,000 children under five are suffering from life-threatening severe acute malnutrition, a 57% increase compared with 2015.
Last week, the UN said an estimated 63,000 children had died in 2016 of preventable causes often linked to malnutrition, such as diarrhoeal diseases, malaria and respiratory infections.
The BBC's Imogen Foulkes in Geneva says the UN hopes its appeal will be fully funded quickly. But money is not the only hurdle, our correspondent adds.
Yemen's air and sea ports are regularly blocked by the warring parties, and supplies can often not get in. A UN-sponsored peace process also appears stalled.
The aid agency Oxfam has accused countries who could be helping end the war - including the UK, which has supplied arms to Saudi Arabia - of "complicity".
"Many governments have weighed their narrow national interests in the Middle East against humanity, and humanity has lost," it said on Wednesday.
The UN has appealed for $2.1bn (Â£1.7bn) to provide life-saving assistance to 12 million people in war-torn Yemen who it says face the threat of famine.