The doctor died after he was infected by a man linked to the first case in Africa's most populous country, the Health Ministry said on Thursday.
Heath Ministry spokesman Dan Nwomeh said on his Twitter feed that the doctor had treated a primary contact of Patrick Sawyer, the Liberian who brought Ebola to Lagos. His death brings the number of Ebola fatalities in Nigeria to 6.
The total number of recorded cases had risen by two to 15, Nwomeh said, the other one being the wife of the doctor who is showing Ebola symptoms and whose test results are awaited.
Port Harcourt lies at the heart of Nigeria's two million barrels per day oil industry, Africa's biggest, and is a hub for expatriate workers in major international oil companies.
Nwomeh said 70 contacts of the doctor were now under surveillance in Port Harcourt.
It was not immediately clear what impact the arrival of Ebola would have on oil operations. The majors operating in Nigeria have historically been comfortable with a fair degree of risk in the oil producing Niger Delta, including attacks on oil installations and rampant kidnapping of expatriates.
The news came two days after Health Minister Onyebuchi Chukwu said authorities had "thus far contained" the Ebola outbreak in Africa's largest economy, with only one case left being treated in an isolation ward in Lagos.
All Nigerian cases have been direct or indirect contacts of Sawyer, who collapsed on arrival at Lagos airport on July 25 and later died but was treated before anyone knew what he had.
The Ebola outbreak in West Africa has taken 1,552 lives out of 3,069 known cases in four countries and "continues to accelerate", the World Health Organisation (WHO) said on Thursday.