The region has been ravaged by a decade-long insurgency by Boko Haram jihadists that has forced around 1.8 million people from their homes.
Aid workers fear the virus could prove devastating if it spreads inside the crowded camps holding hundreds of thousands of displaced people.
The Nigeria Centre for Disease Control said on Twitter that it had recorded one case of the disease in Borno state, the epicentre of the conflict.
Doctors Without Borders (MSF) said in a statement that one of its staff died on April 18 in the state capital Maiduguri “and post mortem test results indicated that they were positive for Covid-19”.
The international aid group said it was supporting Nigeria’s health ministry “in contact tracing”.
MSF insisted it “will continue to operate, providing essential treatment for communities in Nigeria”.
“In all our projects and in order to protect our staff and patients, MSF teams have strengthened infection prevention measures, hygiene facilities, infection control and the establishment of isolation spaces,” it said.
Ten years of conflict in northeast Nigeria has left the region in no state to deal with a global pandemic.
Only half of the roughly 700 health facilities in Borno state are still working and many have been damaged by the fighting.
Humanitarian workers fear increased restrictions over the virus could hamper efforts to reach an estimated 7.1 million people in desperate need of assistance.
Nigeria has so far confirmed 627 infections from the novel coronavirus, with 21 deaths, across the country.
Download our app and read this and other great stories on the move. Available for Android and iOS.