The 74-year-old leader, who has been out of the country for two weeks, was expected to return to Abuja on Sunday.
An official statement said he had been advised by doctors to await the results of a series of tests.
However, it did not say how much extra time would be needed.
There was also no mention of what the medical checks were for.
Analysts say that Mr Buhari's extended absence could further erode confidence in his administration which is already under pressure due to a weak economy and the conflict with Boko Haram Islamist militants in the north-east of the country.
The country is currently suffering from its worst economic crisis in years, following a sharp in the price of oil, its major export.
Businesses and investors complain that the government's handling of the currency exchange rate has made a bad situation even worse, and there have been demonstrations against the lack of jobs and high inflation.
Vice-president Yemi Osinbajo is taking on presidential responsibilities while the president is abroad.
It is the second time in less than a year that Mr Buhari has sought medical assistance overseas. Last June, he spent nearly two weeks, again in London, for treatment for an ear infection.
The trip to the UK appears to roll back on the commitment to tighten up on government officials seeking medical attention abroad.
Speaking on the president's behalf at last year's Nigeria Medical Association General Conference (NMA) in Sokoto, Health Minister Isaac Adewole said the Buhari administration would not encourage spending Nigeria's hard earned resources on any government official seeking medical care abroad, especially when there was evidence of expertise in Nigeria.
The president has been heavily criticised for seeming to renege on his promise to restrict "medical tourism".
After the first visit to London, leading Nigerian doctor Osahon Enabulele, vice-president of the Commonwealth Medical Association, said it was a "national shame" that Mr Buhari went to the UK for treatment when Nigeria had more than 250 ear, nose and throat (ENT) specialists, as well as a National Ear Centre.
He said also that Mr Buhari should lead by example in using Nigerian doctors and facilities, and ensure government officials do not go abroad on "frivolous" medical trips.
In the past, President Buhari has said that Nigeria loses about $1bn a year to medical tourism.