The Duke of Edinburgh is responding well to treatment but it is unclear when he will be discharged, Buckingham Palace said on Thursday.
The palace said Prince Philip is likely to remain in hospital for a few more days.
The Duke was spotted at an Olympic boxing match earlier this month
On Wednesday it was announced Philip had a recurrence of the bladder infection that he suffered in the summer and has been admitted to hospital for investigation and treatment.
The Duke was taken to Aberdeen Royal Infirmary on Wednesday afternoon. A spokesman said Philip travelled to the hospital, about 40 miles away from Balmoral where he was staying with the Queen, by road.
The Duke went to Balmoral after attending a number of Olympics events, including granddaughter Zara Phillips' Olympic debut on 29 July.
Prince Philip was also taken to hospital in June with a bladder infection
He was forced to miss some of the jubilee celebrations in June after he was admitted to hospital the day after braving the elements for the pageant.
Philip was at the Queen's side during the Opening Ceremony of the London Olympics on 27 July and the following when they toured the Olympic Park.
While in Scotland earlier this month he supported the Queen at engagements including hosting a tea party at Balmoral to mark the end of her Diamond Jubilee celebrations.
The hospital admission comes little more than a week after the Duke made a public appearance at a garden party in the north-east of Scotland.