Saifura Hussaini Ahmed Khorsa, 25, was kidnapped by suspected Boko Haram militants in March this year alongside two other ICRC aid workers during an attack on a military facility.
At least three Nigerian aid workers were killed and three others were injured in the attack.
The ICRC condemned the killing and said it was "devastated" by the news.
"We are devastated by the murder of our colleague Saifura," said Eloi Fillion, head of ICRC delegation in Abuja.
"Saifura moved to Rann to selflessly help those in need. Our thoughts are with her family and other loved ones at this incredibly difficult time," he added.
The ICRC said it will not comment on the "motives or the details" surrounding the nurse's death, and called for the immediate release of the two aid workers still held by the group.
"We urge those still holding our colleague Hauwa and Alice: release these women. Like Saifura, they are not part of the fight. They are a midwife and a nurse. They are daughters, a wife, and a mother -- women with families that depend on them," said Fillion.
"Their families and friends miss them dearly and will not give up the hope of seeing them again soon. There is no ideology or religious law that could justify doing any harm to them," he added.
Khorsa was working in the UNICEF clinic in Rann with internally displaced people in a remote town outside Maiduguri, in Nigeria's troubled north east region.
Her death comes as a local publication reported it had obtained a video that showed the aid worker being shot by the militants.
In the video, the insurgents alleged the Nigerian government ignored messages and audios it had sent showing that the aid workers were still alive, according to the report.
The report also stated that the kidnappers threatened to kill the two remaining health workers and kidnapped schoolgirl Leah Sharibu, who remains in Boko Haram camp because she reportedly refused to denounce her Christian faith.
Around 3,000 aid workers, most of them Nigerian nationals, work in Nigeria's northeast.
Boko Haram fighters who have waged a decade-long war in the region regularly attack such camps with gunmen and suicide bombers.