Officers are attempting to rescue the four, who were taken by unidentified gunmen in the southern Delta state.
Police said the kidnapping took place on October 13 but was only now being made public.
A police spokesman said: ”The abductors have not made any contact.
“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.”
He said the British nationals had been working in a very rural area.
Kidnapping for ransom is a common problem in parts of Nigeria.
Several foreigners have, in the last few years, been kidnapped in the Niger Delta region.
The area holds most of the country’s crude oil, the country’s economic mainstay.
There was an increase in crime in the southern region last year that coincided with a series of attacks on energy facilities.
However, there have been no militant attacks on energy installations so far this year.