None of the contacts, who are now in isolation, are known to have developed symptoms, including the person the patient travelled with, the health minister said, adding that the woman had not travelled outside Abuja since landing.
Kaseya explained that the woman had first developed symptoms on 6 October when she had sought medical help.
“She went to the first hospital, a private hospital, thinking that she had malaria, and then she went to the second private hospital. She was admitted on the 11th,” he told the BBC’s Newshour programme.
Malaria is endemic in Nigeria and its symptoms – a high temperature, headaches, muscle aches, vomiting and or diarrhoea – are similar to those of Ebola.
After her condition failed to improve, public health authorities were alerted on Monday 19 October, Pate said.
Her diagnosis was confirmed the next day following three laboratory tests, he said.
The incubation period for Ebola ranges from two to 21 days, meaning those exposed to the virus may not become ill for several weeks.
Ebola is a rare but deadly disease, external caused by a virus. As the disease progresses, vomiting and diarrhoea develop and it can lead to organ failure. Some, but not all, patients develop internal and external bleeding.
The disease spreads from one person to another by contact with infected bodily fluids such as blood or vomit.
The outbreak in Democratic Republic of Congo, which began in May, has claimed at least 4,600 lives, with more than 9,500 cases recorded, the European Centre for Disease Prevention and Control reports, external.
Shortly after the outbreak was announced, it was also reported in Uganda, where at least two people died. Uganda declared itself free of the disease in August after its last patient was discharged.
There have been conflicting accounts about the patient in Nigeria and her movements.
Pate and Kaseya’s comments contradict a statement issued earlier by the Ugandan ministry of health, which described the woman as a Nigerian national who had gone to eastern DR Congo for business, only transiting through Uganda.
It insisted there were currently no confirmed active Ebola cases in the country and that the woman’s passage through Uganda did not mean she had contracted the virus there.
Nigeria’s health minister and the Africa CDC chief have sought to play down any tension.
Pate said Nigerian officials were working with Uganda, Ethiopia and the Africa CDC to establish the full facts.
“We respect our sister nation of Uganda,” he said. “We have very strong solidarity, we are all in it together.”
Kaseya also urged African countries to share information, saying this would help investigators trace the woman’s movements and establish where she might have contracted the virus.
And he encouraged Western countries not to impose travel restrictions, saying “collaboration and solidarity” were the way to help stop the current outbreak.
The disease recently spread to Kenya, which has reported at least nine infections.
On Monday, the US advised its citizens to reconsider travel to Kenya because of health risks and raised its travel advisory level for the country.
In 2014, Nigeria successfully contained an Ebola outbreak, which had resulted in 20 confirmed cases and eight deaths.
Pate expressed confidence in the country’s ability to repeat that success, citing strengthened disease surveillance, laboratories and thousands of trained epidemiologists.
“Nigeria has muscle memory that has been activated, but we are not fighting the past outbreak in the exactly the same way. We have to be vigilant,” he said.
The outbreak in DR Congo has been caused by the Bundibugyo species of Ebola, which is relatively rare, with no approved vaccine or treatment – though trials are under way.
Additional reporting by Timothy Obiezu and Lucy Fleming
