Prince Philip was admitted to hospital for an exploratory abdominal operation on the evening of June 6.
The Duke of Edinburgh was taken to the Harley Street's London Clinic shortly after making an appearance at the Queen's garden party at Buckingham Palace.
The Duke, who turns 92 on 10 June, is expected to remain there for up to two weeks.
He missed an engagement on Monday night because he was feeling "under the weather".
"He is in very good health," a Buckingham Palace spokesperson said. "He felt unwell on Monday and missed an engagement but that was down to the fact he had temporarily lost his voice."
His admission to hospital was planned for after the garden party. The Palace said in a statement that "further updates will be issued when appropriate".
Philip and the Queen appeared on the steps of the Palace at 4pm when the national anthem was played to mark the start of the third of the summer garden parties. Onlookers reported Philip being in good spirits as he mingled with invitees. He was also later invested with his Additional Member of the Order of New Zealand award by the Queen in a ceremony at Buckingham Palace.
On Wednesday, he toured a Victorian steamship, the SS Robin, in London's East End. It was a very personal visit for the former sailor who led a campaign against the vessel being scrapped in the 1970s.
The Queen will still conduct her engagements as planned on Friday, which include a visit to the new BBC studios in London.
Prime Minister David Cameron wrote on Twitter, "My best wishes to the Duke of Edinburgh who is in hospital tonight. I hope he has a swift recovery."
The couple, who have been married for 65 years, attended the service to mark the 60th anniversary of the Queen's coronation on Tuesday after much speculation that the Duke would be unable to attend due to his health problems.
Last summer, the 91-year-old spent five nights in hospital and missed some of the events for the Queen's Diamond Jubilee celebrations due to a recurring bladder infection.