Prince Philip, 99, was taken to the King Edward VII Hospital in London, the statement added.
A palace source told the BBC that he travelled by car to the hospital, where he was admitted on his doctor's advice.
The duke had been feeling unwell for a few days, but it was not related to coronavirus, the source added.
It added that he was "in good spirits" in hospital, where is expected to remain for a few days of observation and rest.
The duke walked into the hospital.
The Queen, 94, remains at Windsor.