The Queen made the short journey from Buckingham Palace to Kensington Palace, William and Kate's home in central London to see the baby, the third in line to the British throne after Prince Charles and Prince William.
She visited without her husband, the Duke of Edinburgh, as he continues to recover from abdominal surgery.
A Kensington Palace spokesman said it was "now private and quiet time for them to get to know their son".
The 87-year-old monarch had said she was "thrilled" at the arrival of her third great-grandson during a reception at Buckingham Palace yesterday.
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Earlier, the Queen had said that she hoped to be able to see the baby before setting off on her summer break and the new royal baby seems to have followed her orders.
Shortly after the Queen's visit, the Duke and Duchess of Cambridge left Kensington Palace to pay a visit to Middleton's house in Bucklebury with their newborn son.
The Queen was not the first visitor to meet the royal baby prince. The Prince of Wales and Duchess of Cornwall, and Catherine's parents, Carole and Michael Middleton, paid visits to the hospital yesterday afternoon.
He had triggered a frenzy among the waiting reporters and camerapersons as he said on his departure: "He (royal baby) is marvellous. You will see in a minute".