"This new case is one of the doctors who attended to the Liberian Ebola patient who died," said Health Minister Onyebuchi Chukwu.
The minister told journalists that 70 other people believed to have come into contact with the Liberian are being monitored, eight of whom have been placed in quarantine at a facility in Lagos.
Patrick Sawyer, who worked for Liberia's finance ministry, contracted the virus from his sister before travelling to Lagos for a meeting of west African officials.
He landed in Lagos on July 20 from Monrovia after switching planes in Togo's capital Lome.
He was visibly sick upon arrival and taken directly to the First Consultants hospital in the upmarket Lagos neighbourhood of Ikoyi. He died in quarantine on July 25.
The hospital was closed indefinitely last week.
The second confirmed case in Nigeria is the latest in the deadliest-ever Ebola outbreak, which has infected 1,440 people and left 826 dead. The other cases are spread across Guinea, Liberia and Sierra Leone.