The man was admitted to the University Hospital Zurich while his wife was taken for treatment at the Geneva University Hospital, the canton of Geneva said.
"This situation does not pose any risk to public health in Switzerland," the Swiss government said in a statement.
The Ugandan-born wife of the diplomat, based in Abuja, was being treated for the Bundibugyo strain of Ebola, which has caused an outbreak that started in Democratic Republic of Congo.
Her husband, considered a close contact, was in isolation at the Zurich hospital, the Swiss Federal Office of Public Health said.
Both hospitals are equipped to handle such cases without endangering others, it said.
Nigerian Health Minister Muhammad Ali Pate had said the woman's clinical condition was much improved.
It is Nigeria's first Ebola case in more than a decade.
The disease has now been reported in east, central and west Africa, giving it the widest geographic spread of any Ebola outbreak on the continent to date.
The possibility that the woman might have been infected in Uganda, where officials say she spent a two-week holiday before returning to Abuja, has fuelled concerns about undetected transmission in a country where the outbreak had appeared to be under control.
Pate said the woman was "stable, conscious, communicating" and that her test results were reverting towards "baseline".
He husband had no symptoms and left Nigeria on the same flight, Pate added.
Experts will travel to Nigeria to help investigate how the patient caught the virus, Africa CDC director-general Jean Kaseya told Reuters.
He said her travel documents showed she had not visited DR Congo, contradicting statements from Ugandan officials.
There are no approved vaccines or treatments for the Bundibugyo strain, which has caused almost 10,000 cases and more than 4800 deaths in Congo.
Kenya has reported nine cases and two deaths, all linked to a man who had travelled from DR Congo via Uganda's Entebbe airport.
Uganda reported 20 cases in May and June but has not recorded any since.
The World Health Organisation declared it free of the virus in August.
The WHO's Africa director Mohamed Janabi congratulated Nigeria's government and health workers on stabilising the patient's condition, allowing her to be transferred overseas.
