It follows concerns highlighted in a recent UN committee report about race discrimination.
It also recognises the recent sharp increase in racist hate crime following the EU referendum.
The report also calls for better accommodation for the traveller community in Northern Ireland.
Northern Ireland's traveller community still faces problems with health, education, housing and employment, adds the UN report.
NIHRC chief Les Allamby welcomed the call supporting Northern Ireland's travellers.
"The committee has highlighted the disparity in equality protection between Northern Ireland and the rest of the UK, calling for a Single Equality Bill to address this problem," he said.
"We raised these concerns directly with the committee in July and welcome that they have been incorporated into the UN report.
"We now need action to be taken by the Northern Ireland Executive to tackle these important issues and improve the quality of life and experiences of people from minority ethnic backgrounds in Northern Ireland."
The Northern Ireland Human Rights Commission has called on the Executive to do more to improve life for people from minority ethnic backgrounds.