A spokeswoman for the Office of UN High Commissioner for Refugees (UNHCR) said that over 900 people from Mosul had crossed the border into Syria and were now at a refugee camp.
She said it was likely the agency would use the camp as a staging-post before moving back across the border to a safe location in Iraq, the BBC’s Richard Galpin reports.
The movement of a significant number of people indicates that IS militants are not able to stop everyone leaving, our correspondent notes.
It will also raise questions about whether some fighters might try to use the same route to flee, he adds.
In the US, Pentagon spokesman Navy Captain Jeff Davis warned on Tuesday that the IS would use civilians as human shields.
And the International Organization for Migration fears IS might even use chemical weapons.
Residents reached by telephone by Reuters news agency said IS was preventing people fleeing the city and had directed some of them towards buildings likely to be targeted by air strikes.
US President Barack Obama said it was important to ensure that Mosul’s residents can safely flee the city.
“If we aren’t successful in helping ordinary people as they’re fleeing Isil (IS), then that makes us vulnerable to seeing Isil return,” he told reporters in Washington.
The UN is working to create new refugee sites outside Mosul.
Lise Grande, the UN’s humanitarian co-ordinator for Iraq, said the organisation was working on the assumption that as many as 200,000 people might need shelter in the first days and weeks of the operation.