With much of the country dependent on aid, a coronavirus pandemic raging unchecked, and countless children already facing starvation, Lise Grande said that millions of vulnerable families could quickly move from "being able to hold on to being in free fall."
The United Nations raised only around half the required $2.41 billion in aid for Yemen at a June donor conference.
Yemen is already gripped by what the UN calls the world's worst humanitarian crisis, with tens of thousands killed, an estimated four million people displaced by war and 80 percent of the country's 29 million people dependent on aid for their survival.
Grande told AFP in an interview from Sanaa that critical programs providing sanitation, healthcare and food were already closing down because of a lack of cash, just as the economic situation is looking "scarily similar" to the darkest days of the crisis.
A critical fuel shortage is now threatening the operation of the electricity grid, water supply, and key infrastructure like hospitals.
"Ships aren't being allowed to bring in life-saving commodities, the currency is depreciating very quickly. The central bank is out of money. The price of a basic food basket... has increased by 30 percent in just the past few weeks alone," Grande said.
"We're seeing the same factors driving the country towards famine that we saw before. We don't have the resources we need to fight it and roll it back this time. It's something to be profoundly worried about."
Grande said that only nine of the 31 donors had actually provided the funds -- a pattern that the UN has sounded alarm over before, and which will worsen as the world sinks into a coronavirus-induced recession.
"It's very clear that the COVID pandemic has put pressure on assistance budgets all over the world ... They're just not going to be able to do what they've done previously. And the impact of that is going to be very significant, very severe," she said.
Yemen has so far officially recorded some 1,300 cases of the disease, with 359 fatalities, but testing is scant, most clinics are ill-equipped to determine causes of death and there are ominous signs that the real toll is much higher.
Modeling by the London School of Hygiene and Tropical Medicine indicates there could have been over one million coronavirus infections by last month, and that 85,000 people could die in a worst-case scenario. But as the country's needs escalate, the ability to meet them has diminished.
- Programs cut -
Grande said that in the next few days, the UN faced the "unbelievable situation" of having to stop providing fuel to hospitals as well as water supply and sanitation systems across the country.
The World Food Program, which has been providing staples to 13 million people, has had to scale back with deliveries to only about 8.5-8.7 million people per month, and many of those have been put on half rations.
And the week the coronavirus crisis started, the WHO ran out of funds to pay 10,000 public health workers across the country.
A year and a half ago when Yemen last stood on the brink, the situation was very different.
"Eighteen months ago, we were one of the best funded humanitarian operations in the world," Grande said.
"The country is right back where it was. The difference is that now we don't have the resources we need in order to push it back."
Saudi Arabia and a number of its regional allies launched a devastating war on Yemen in March 2015 in an attempt to subdue an uprising that toppled a regime friendly to Riyadh.
The US-based Armed Conflict Location and Event Data Project (ACLED), a nonprofit conflict-research organization, estimates that the war has claimed more than 100,000 lives over the past five years.
More than half of Yemen’s hospitals and clinics have been destroyed or closed during the war by the Saudi-led coalition, which is supported militarily by the UK, the US and other Western countries.