Questioned by journalists while visiting a vaccination centre in eastern England, second-in-line to the throne William, 38, said: "Yes, he's OK, they're keeping an eye on him."
He then gave a wink.
Prince Philip, Queen Elizabeth II's husband for 73 years, was admitted to the private King Edward VII Hospital in London on Tuesday evening as a "precautionary measure" after he felt unwell, Buckingham Palace said.
Palace sources said that his admission was not coronavirus-related and that he was in good spirits.
William's father Prince Charles visited his father in hospital on Saturday but did not comment on his state of health.
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