A senior public health official told a local television station the woman was "originally from Uganda and so made a quick travel to Uganda".
Uganda's health ministry said she had travelled to the Democratic Republic of the Congo, which is battling the world's second-largest Ebola outbreak on record with more than 9000 cases and more than 4000 deaths.
Odianosen Ehiakhamen, the assistant director of the Nigeria Centre for Disease Control and Prevention, told Arise TV the Ebola patient arrived in Nigeria on October 5 and started feeling unwell on October 7.
She sought treatment at a private hospital on October 11 for malaria-like symptoms and was tested for Ebola on October 19, Ehiakhamen said.
Most of the 44 contacts traced so far are healthcare workers and the patient's husband, a Swiss national who lives with her in the capital, Abuja.
Health authorities are also tracing passengers who travelled with her on the same Ethiopian Airlines flights from Uganda but they do not think she was symptomatic while flying.
Nigerian Health Minister Muhammad Ali Pate told public broadcaster NTA that the woman was in isolation and receiving quality medical care.
Uganda's health ministry said in a statement that "travel through Uganda does not establish that infection occurred here."
It said Uganda had "no confirmed active Ebola cases".
Pate said Nigeria had successfully contained Ebola in 2014 and had the systems in place to respond to the new case.
Congo's Ebola outbreak was declared in mid-May but might have started months earlier, caused by the rare Bundibugyo strain.
Uganda reported 20 cases in May and June, mostly imported from Congo, but was declared free of the virus by the World Health Organisation in August.
Kenya has reported nine Ebola cases in October, all linked to a person who had travelled from Congo.
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