The Duke, who has retired from royal duties, has been absent from various events in recent days, most recently the Easter Matins Service at St George's Chapel, Windsor Castle, on Sunday.
He also missed the annual Maundy Service at Leicester Cathedral last Thursday because of his hip problem, despite being named as a guest in the order of service.
Last week, he pulled out of an official engagement with the Queen and Duke of York because he was unwell, according to reports.
However, he was spotted driving in Windsor Great Park on Wednesday.
The Duke has been admitted to hospital with various ailments over the years including bladder infections, a blocked coronary artery and for abdominal surgery.
He was last admitted in June, after becoming ill with an infection arising from a pre-existing condition.
He spent two nights at the King Edward VII hospital as a precautionary measure on the advice of a doctor.
Peter Kay, professor of orthopedics at Manchester University and a council member of the Royal College of Surgeons, said the most common reason older patients were admitted for hip surgery was for a hip replacement, usually because of osteoarthritis or a fracture.
He said between 1 and 2 per cent of hip replacements were performed on people in their 90s and that the mortality rate had halved in the past few years to just 0.25 per cent.
"It is a relatively safe procedure," he told the Telegraph.
"You have to make sure the patient is fit and well but generally speaking, you will be in hospital about five days and spend six to eight weeks using crutches before walking independently and carrying on with normal life."
The Queen Mother had a right hip replacement at the same hospital in 1995, at the age of 95, and her left hip replaced, aged 97, in 1998.
Other procedures include a partial hip replacement or treatment for other illnesses such as cancer or an infection.
The Duke retired from royal duties last August. Buckingham Palace stressed that the decision was not health-related and that he had the full support of the Queen.