The council, which has been operating since 1994, said in a letter that it cannot stay open because of a "severe cash-flow problem".
It said that it had failed to gain two Stormont grants that would have totalled Â£90,000.
Patrick Yu, the council's executive director, said closure was a "painful decision".
"This is the best way to protect the achievement, reputation and integrity of NICEM," he said.
In the letter, he said that while NICEM had "several outstanding funding applications" it was "unable to sustain a sufficient cash flow".
He said the council would be dissolved after a general meeting on 7 November.
He added his thanks to those who had joined "our anti-racist movement".
"Despite this set back, the vision and values of NICEM will continue as well as the anti-racism movement in Northern Ireland."
Northern Ireland's Council for Ethnic Minorities is set to close because of a lack of funds.