She was struck down by the stomach bug on Friday and admitted to King Edward VII's Hospital in central London yesterday as a "precaution", but is "otherwise in good health", according to a spokesman.
The Queen was well enough yesterday to meet an employee privately to award her a medal for long service before travelling by private car to the hospital.
"There was never any suggestion at all of an ambulance taking her," a Buckingham Palace spokeswoman said.
She is likely to stay at the hospital for two days, so has been forced to cancel a visit to HMS Lancaster, in London today.
A reception she was to hold for MPs and MEPs at Buckingham Palace will now be hosted by another member of the Royal Family.
A two-day tour to Rome with the Duke of Edinburgh, which was due to begin on Thursday, has also been called off to allow the 86-year-old monarch to rest.
A Palace spokesman said: "The Queen is being assessed at the King Edward VII's Hospital, London, after experiencing symptoms of gastroenteritis.
"As a precaution, all official engagements for this week will regrettably be either postponed or cancelled."
The spokesman added: "This is a precautionary measure.
"She was not taken into hospital immediately after feeling the symptoms.
"This is simply to enable doctors to better assess her."
Buckingham Palace confirmed that the Duke of Edinburgh will undertake a solo public engagement today.
He is due to attend an event as an honorary member of the Imperial Poona Yacht Club at the Royal Thames Yacht Club, in London's Knightsbridge.
It is the first time the Queen has been admitted to hospital in nearly 10 years.
She last had a hospital stay in December 2003 for an operation on her left knee. It is believed the Queen will not be receiving visitors.
A royal source said: "She is very much known for not making a fuss."
Downing Street said Prime Minister David Cameron had passed on his best wishes to the Queen.
A handful of police officers stood guard at the entrance to the hospital last night, while a pack of television crews, photographers and reporters waited outside.