“The needs are rising exponentially and we are broke,” said Marixie Mercado, a spokeswoman for children’s charity Unicef.
Some 1.2 million Syrians have fled since the uprising began in March 2011.
Around 385,500 have escaped to Jordan, with figures set to triple by the end of the year, Ms Mercado said.
This would bring the number of Syrian refugees there close to 1.2 million – the equivalent of one-fifth of Jordan’s total population.
“Since the beginning of year, more than 2000 refugees have streamed across the border [into Jordan] every day,” Ms Mercado told reporters at a UN news conference in the Swiss city of Geneva on Friday.
“We expect these numbers to more than double by July and triple by December.”
Many of the refugees are children, the spokeswoman added.
Unicef is currently providing water, sanitation, vaccines, education and other essential services in Jordan’s Zaatari camp, which houses nearly 150,000 refugees.
So far the agency has only received $12m (£7.8m), or 19%, of the $57m it appealed for to fund its Jordan operations this year.
As a result, it will soon need to “scale back life-saving support”, Ms Mercado said.
“In concrete terms, this means that by June, we will stop delivering 3.5m litres of water every day to Zaatari camp.”
She added that the money shortage also meant Unicef would be unable to provide supplies to two new camps slated to open in the coming weeks.
UN officials said the lack of funding did not only apply to Jordan, but also to other countries hosting large numbers of Syrian refugees, including Lebanon, Turkey and Iraq.
“It is unmanageable and dangerous.”
The UN estimates that at least 70,000 people have been killed in Syria since the uprising against President Bashar al-Assad began, just over two years ago.