The half-hour visit to Kensington Palace came after Prince William, Kate Middleton and the royal baby spent their first night at home.
They left St Mary’s Hospital in west London on Tuesday evening, where Prince William told reporters they were yet to name the third in line to the throne.
The Queen visited without her husband, the Duke of Edinburgh, as he continues to recover from abdominal surgery.
She made the short journey from Buckingham Palace in a dark green Bentley.
The private meeting comes as the monarch prepares to leave for Balmoral in Scotland on Friday, where she has her traditional summer break.
The Queen had said she was “thrilled” at the arrival of her third great-grandchild during a reception at Buckingham Palace on Tuesday evening.
Louise Butt, a guest at the event for the Queen’s Award for Enterprise, said the monarch had also described the baby as a “big boy” and had said that “the first born is very special”.
There has been no word yet from the duke, who is expected to take about two months to convalesce following exploratory abdominal surgery last month.
The Queen was not the first to meet the royal baby prince.
Prince Charles and Camilla, and Kate’s parents, Carole and Michael Middleton, paid visits to the hospital on Tuesday afternoon.
Later that day, Kate’s sister Pippa Middleton, accompanied by boyfriend Nico Jackson, went to Kensington Palace to meet her day-old nephew.
Prince Charles said the baby was “marvelous” while Carole Middleton said he was “absolutely beautiful”.
Prince William was at the hospital for the birth at 16:24 BST on Monday, and stayed with his wife and son, who weighed 8lb 6oz (3.8kg), overnight.
They left at 19:15 BST on Tuesday – just under 27 hours after the baby’s arrival.
Kate Middleton and Prince William described becoming parents as “very emotional”.
A Kensington Palace spokesman said on Wednesday it was “now private and quiet time for them to get to know their son”.
Although the couple have yet to decide on a name it is known that the newest royal will be known as HRH Prince (name) of Cambridge.
George is the bookmakers’ favorite for the first name of the prince, who is destined to be king one day. James and Alexander are among other names on a short price.
Royal fans waited seven days before the name of a newborn Prince William was announced in 1982, and there was a wait of a month following the Prince Charles’s birth in 1948.
All births in England, Wales and Northern Ireland, regardless of parentage, must be registered within 42 days at the hospital or a local register office.
DRNwcqHKrnQ 7qFIrUOQEhAAt least 158 people have died in Spain's worst flooding disaster in generations. On October…
Google has been fined two undecillion (a two followed by 36 zeroes) roubles by a…
Embarking on a home remodel is an exciting journey, promising enhanced comfort, increased property value,…
The US presidential candidates continued to campaign across key swing states on October 20. Footage…
Elon Musk has said he will give away $1 million a day to a registered…
India and Canada have decided to expel their top envoys along with other diplomats as…