Prince Philip was admitted to the King Edward VII's hospital as a precaution on Tuesday.
A Buckingham Palace source told the BBC the duke is likely to remain in hospital into next week.
The exact reason for his admission has not been disclosed but his stay is not related to coronavirus.
A palace source previously said the duke, who is due to turn 100 in June, had walked into the hospital in Marylebone unaided.
Prince Charles, 72, spent about 30 minutes at the hospital on Saturday afternoon. He returned to his Highgrove residence after the visit, a Clarence House spokesman said.
Under England's current coronavirus lockdown rules, visiting someone in a hospital is considered a "reasonable excuse" to leave home, although many hospitals have put significant limits on visitors.
The King Edward VII's hospital website says visitors "will only be considered in exceptional circumstances" during the pandemic.
Members of the Royal Family have continued with their official duties while Philip has been in hospital.
The Queen, 94, performed her first face-to-face event of the year on Thursday, when she knighted a royal aide during a private socially-distanced ceremony at Windsor.
Prince Charles visited the Queen Elizabeth Hospital in Birmingham with the Duchess of Cornwall on Thursday, where he told NHS staff the country owes them "an enormous debt of gratitude" for their efforts in the coronavirus pandemic.
The Duke of Cambridge has also carried out several virtual conversations with frontline NHS staff this week, while the Princess Royal held a virtual meeting in her role as patron of the Scottish Rugby Union.
Last month, Buckingham Palace announced that Prince Philip and the Queen had received Covid vaccinations from a household doctor at Windsor Castle.
The couple have been spending the recent lockdown in England at Windsor with a small household staff, nicknamed HMS Bubble.
They celebrated Christmas quietly there, instead of the traditional family gathering at the Queen's Sandringham estate in Norfolk.
He was discharged on Christmas Eve that year, after four nights and driven to Sandringham, where he spent Christmas with the Queen.
The duke has received treatment for various other 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.
Last November, the Queen and Prince Philip marked their 73rd wedding anniversary by releasing a photograph of themselves opening a card made for them by their great-grandchildren, Prince George, Princess Charlotte and Prince Louis.