gfzdgfsgdhe order came after the International Criminal Court (ICC) issued an arrest warrant for Sudanese President Omar al-Bashir over alleged war crimes.
Aid agencies have expressed concern over the potential impact of the move on thousands of displaced people.
The African Union and Arab League have said they will ask the UN to defer the warrant for a year, saying that arresting Mr Bashir could derail attempts to bring stability to Sudan.
A statement from Mr Ban's office said the decision to expel 13 non-governmental organisations "will, if implemented, cause irrevocable damage to humanitarian operations there".
"The operations of these agencies are key to maintaining a lifeline to 4.7m Sudanese people who receive aid in Darfur," it said.
The statement also expressed concern about the safety and security of national and international humanitarian workers in Sudan and their assets.
"The confiscation of equipment, money and other materials is unacceptable and must end immediately," it said, while stressing that the agencies involved affected had acted "in a neutral and impartial manner".
Among the international aid groups ordered out of Darfur are Oxfam, Care, Medecins Sans Frontieres and Save the Children UK.
Sarah Jacobs of Save the Children Africa told the BBC that children in Sudan would suffer if the charity was prevented from operating in the country.
"We support 50,000 children, trying to protect them from abuse, from physical and sexual violence, trying to get them back into school," she said.
FROM THE BBC WORLD SERVICE
"These are very traumatised children, many of them, and it's essential that Save the Children UK and other aid organisations are able to deliver essential aid to communities, otherwise life is going to get even worse for them.
"Our job now is to make sure that we appeal against that request and that we stay to support the children that we're looking after across the country."...