David Donovan, a former GP from Cambridge, and his wife Shirley, both 57, were snatched from their lodgings in the middle of the night.
Over the last 14 years their charity New Foundations has been providing medical care to remote villages in the Niger Delta.
During one 24 month period they treated 16,000 patients, carried out 500 cataract operations and vaccinated 4000 children against including malaria.
The couple, who have two sons, were kidnapped at 2am last Friday alongside two other Brits named only as Alana and Tyan.
Andrew Aniamaka, a spokesman for Delta state police, said: “The abductors have not made any contact but we are doing our investigations to know the motive and have them rescued without jeopardising their lives.
“Information available to us shows they are missionaries giving free medical services.
“The victims are of British nationality, two of whom are a couple, and have been rendering humanitarian services in the area for a while.
“But unfortunately, they didn’t let the authorities know of their presence in the area all this while.
“There is a militant group that has been operating in the area and we believe they are the ones behind the abduction.
“Immediately the militants struck, they whisked the victims to the interior regions of the creek where we believe they are being held for the past five days.”
David and Shirley, who live in March, Cambs., set up the Christian medical charity in 2003.
They started by establishing a boat clinic so they could bring specialist aid to remote villages.
By 2007 they had set up a well-provisioned health centre capable of providing healthcare and medical training to locals.
Fundraising pages show their aim is to ‘share the gospel’ through providing healthcare to Nigerians.
The couple, whose sons Julian, 30, and Aidan, 27, also worked for the charity, were abducted from the Delta state area.
Local police are now trying to free them from their captors.
Zanna Ibrahim, police commissioner for the state, said the kidnappings may be linked to government attempts to tackle militancy in the region.
The Delta has a history of separatist movements linked to the poverty of local people.
Mr Ibrahim said: “The kidnap may not be unconnected with the present onslaught on militant activities embarked upon by the military.”
Police chiefs say the kidnapping has “saddened” locals who had been helped by the Donovans’ charity.
Abduction for ransom is becoming an increasing problem in parts of Nigeria.
In recent years several foreigners, including an Italian priest, have been held by militants.
Nigeria was also the scene of the infamous kidnapping of hundreds of schoolgirls in 2014.