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.
Last month, the palace announced that Prince Philip and the Queen had received Covid-19 vaccinations from a household doctor at Windsor Castle.
The couple have been spending the coronavirus lockdown in England at Windsor Castle with a small household staff, nicknamed HMS Bubble.
They celebrated Christmas quietly at their Berkshire residence, instead of the traditional royal family gathering at Sandringham.
A No 10 spokesman said Prime Minister Boris Johnson sent his "best wishes" to the duke as he undergoes "a few days of rest in hospital".
In December 2019, the duke spent four nights at King Edward VII Hospital, where he was admitted as a precautionary measure and treatment for a pre-existing condition.
The treatment he has received for various health conditions over the years include being treated for a blocked coronary artery in 2011, a bladder infection in 2012 and exploratory surgery on his abdomen in June 2013.