The Queen visited the Duke of Edinburgh last evening, his 92nd birthday, and stayed with him at the London Clinic on Harley Street for around half-an-hour.
She took her husband a birthday card, addressed to "HRH The Duke of Edinburgh".
"His Royal Highness The Duke of Edinburgh is progressing according to plans at this early stage. He is comfortable and in good spirits.
"He will remain in hospital for up to two weeks, and it is expected he will then be taking a period of convalescence of approximately two months," Buckingham Palace said in a statement.
Also Read
Her visit followed one by the couple's younger son, Prince Edward, earlier in the afternoon yesterday.
Asked by reporters how his father was, he replied: "Well, thank you."
British Prime Minister David Cameron sent a birthday message to the Duke on Twitter, saying: "Wishing the Duke of Edinburgh a very happy 92nd birthday as he recovers in hospital today."
The King's Troop Royal Horse Artillery fired a 41-gun royal salute at midday in Green Park, near Buckingham Palace, to mark the occasion.
Gun salutes were also fired from Edinburgh Castle in Scotland and Hillsborough Castle in County Down, Northern Ireland.
The Duke had been admitted to the elite London Clinic on Thursday for the pre-arranged operation, which he had under general anaesthetic.
Analysis of the results of the operation are expected to be completed this week and it is believed that Prince Philip has been visited daily by royal doctor Professor John Cunningham.
He was admitted to hospital twice last year because of a bladder infection that forced him to miss the last of the Queen's Diamond Jubilee celebrations.
Despite being admitted to hospital on several occasions in recent years, Prince Philip, known for his active lifestyle, has maintained a busy schedule.