Doctors are treating Prince Philip, 99, for an infection. They will also undertake testing and observation for a pre-existing heart condition, Buckingham Palace said.
The duke is responding to treatment and "remains comfortable", it added.
He is expected to remain in hospital until at least the end of the week.
Philip, who turns 100 in June, was taken to King Edward VII's hospital in London on 16 February as a precaution after feeling unwell. A palace source at the time said the duke had walked into the hospital unaided.
On Monday morning, staff held up umbrellas to screen a person from journalists' cameras by umbrellas as they got into an ambulance outside the hospital in Marylebone.
Philip was transferred about 5km to St Bartholomew's Hospital, also known as Bart's, in the City of London.
St Bart's is a centre of excellence for cardiac care, its NHS site says.
The exact reason for Philip's initial admission has not been disclosed, but his stay is not related to coronavirus.
The Prince of Wales visited his father for around 30 minutes, the weekend after he was admitted.
Two days later the Duke of Cambridge said his grandfather was "OK" and that doctors were "keeping an eye" on him.
The following day, on 23 February, Buckingham Palace said Philip was being treated for an infection and was not expected to leave hospital for several days. The Earl of Wessex added his father was feeling "a lot better" and appreciated the "lovely messages" from the public.
Members of the Royal Family, including the Queen, have continued with their official duties during the duke's hospital stay.
The Queen's engagements over the past two weeks have included hosting a video call with health officials leading the UK's Covid vaccine rollout, and knighting a royal aide during a private socially-distanced ceremony at Windsor.
Prince Philip retired from royal duties in 2017 in a move supported by the Queen.
Known for off-the-cuff remarks at public events, Prince Philip joked at the time that he was the "world's most experienced plaque unveiler".
In his time as a working royal, he has attended over 22,000 solo engagements and given more than 5,000 speeches.
The duke has received treatment for various health conditions over the years, including a blocked coronary artery in 2011, a bladder infection in 2012 and exploratory surgery on his abdomen in June 2013.
Photo AFP caption: Staff use umbrellas to shield an individual wheeled to an ambulance parked outside King Edward VII's Hospital in central London on 1 March.