Buckingham Palace said the surgery went well and that he is "progressing satisfactorily at this early stage" while staying in "good spirits", local news outlets reported.
Buckingham Palace announced on Tuesday that Prince Philip was admitted to King Edward VII Hospital in London, England, for the planned surgery.
On Sunday, he was absent from the Easter service attended by the Queen and other members of the royal family at St. George's Chapel in Windsor - also the venue for Prince Harry and Meghan Markle's wedding on May 19.
Very last June, Prince Philip put in two nights in hospital as a "precautionary measure" to its treating an undisclosed infection.
He is said to be "comfortable and in good spirits".
The exact nature of Philip's hip problem was unclear but Buckingham Palace said an update on his health would be given when appropriate.
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Scarlett McNally, an orthopaedic surgeon and council member of the Royal College of Surgeons, said fitness was more important than age when it came to recovering from surgery.
Philip has sharply reduced the number of charity events he attends since announcing his retirement, but still accompanies the Queen on occasion.
The Duke of Edinburgh pictured at King's Lynn railway station. "But clearly he is getting more frail, and while the Duke remains as active as he can be, this hip operation is a reminder that he isn't getting any younger".
Philip, or the Duke of Edinburgh as he is known in Britain, retired from public life last August. He has carried out some 22,000 solo royal engagements since Elizabeth became queen in 1952.
The British monarch and her husband celebrated their 70th wedding anniversary last November.
The Queen has praised her husband for his devotion and long years of service, calling him the rock she depends on.