The Iraqis recaptured its eastern sector and launched a major operation to recapture west Mosul.
"They are desperate for food. They are panicked," Bruno Geddo, who represents the UN refugee agency in Iraq, told reporters in Geneva by phone from a transit centre for displaced people near Mosul.
He said people arriving at the Hammam al-Alil transit centre about 20 kilometres (12 miles) south of Iraq's second largest city described the desperate situation they left behind.
"There is a shortage of fuel, of food, of electricity. People have resorted to burning furniture, old clothes, anything they can use to keep warm at night, because it is still raining heavily and the temperatures at night in particular drop significantly," he said.
"It is very, very limited what they can eat," he said, adding that people were surviving primarily on a little bread and water, and many were eating just once a day.
His comments came as Iraqi forces, which launched a massive operation to retake Mosul in October, gain ground from IS fighters in the west of the city after taking back the east.
IS overran large areas north and west of Baghdad in 2014, but Iraqi forces have since regained much of the territory they lost.
The Iraqis recaptured its eastern sector and launched a major operation to recapture west Mosul -- the most-populated urban area still held by IS -- on February 19.
They have retaken a series of neighbourhoods from the jihadists.
Geddo said around 600,000 people remained in the 60 percent of west Mosul still under IS control, but that number was constantly changing as people fled.
So far, about 153,000 people have fled western Mosul since February 19, he said.
He said between 8,000 and 12,000 people were arriving at the transit centre each day, many malnourished.
Medical charity Doctors Without Borders also reported that it treated children for "severe malnutrition" after they escaped from Mosul.
Geddo said an increasing number were leaving, with many telling UNHCR staff on the outside that they prefered "to take the risk of dying while I stand a chance to be free and safe again with my family."
Since October, around 340,000 people have fled all parts of Mosul, but 70,000 have returned to the eastern part of the city, leaving about 270,000 displaced, according to UNHCR figures.