Queen Elizabeth II's husband is "comfortable and in good spirits," Buckingham Palace officials said in a brief statement. Details of his condition were not released.
He is expected to stay in a London hospital for about two weeks before going into convalescence. The palace said the queen is expected to visit him there Monday evening.
Philip's son, Prince Edward, was the first member of the royal family to pay a visit. After spending 20 minutes at his father's bedside Monday, Edward told reporters outside the hospital that his father was doing well.
Officials say he is "progressing satisfactorily" after the exploratory surgery on Friday at a private London clinic. Results of various tests are expected this week, but it is not clear if the diagnosis will be made public.
Philip has suffered heart and bladder problems in the past but he appeared well when he was last seen in public at a Buckingham Palace garden party Thursday.
His birthday was officially celebrated by two extended gun salutes in central London.