The figures released in a UN report describe some of the worst conditions yet in more than two years of a civil war marked by atrocities and accusations of war crimes, including the blockading of food supplies.
Conditions are "escalating", the UN said, with already over 2.8 million people needing aid, almost a quarter of the country.
"Nearly 25 per cent of the country's population remain in urgent need of food assistance, and at least 40,000 people are on the brink of catastrophe," the UN's Food and Agriculture Organization (FAO), the UN children's agency UNICEF and the World Food Programme (WFP) said in a joint statement.
"Families have been doing everything they can to survive, but they are now running out of options," said UNICEF country chief Jonathan Veitch.
"Many of the areas where the needs are greatest are out of reach because of the security situation. It is crucial that we are given unrestricted access now."
The warning comes three months after the last UN-backed specialised hunger assessment, the Integrated Food Security Phase Classification (IPC) report. That October report warned of a "concrete risk of famine" without aid.
There has been no let up in the conflict and while some food has been delivered, civilians report dire conditions. The army and rebels have repeatedly accused each other of breaking an internationally-brokered August ceasefire.
The IPC lists famine as a technical measure, which classifies hunger on a scale of one to five. Level five is classified as "catastrophe", and when stretched to 20 per cent of the population, becomes famine.
A year ago famine was averted only after a huge intervention by aid agencies. Those worst affected are in the northern battleground state of Unity, once the country's key oil producing region, but now scene of some of the heaviest fighting, including the mass abduction and rape of women and children.
The counties of Mayendit, Koch, Leer and Guit are hardest hit. The UN said conditions are "particularly worrisome" because they show an increase in hunger during the post-harvest period, when people should have the most food, warning that the hunger season will start earlier and last longer than normal.