The King and Queen, the Duke of York, Duke of Edinburgh and the Prince of Wales were informed on Sunday evening and the monarch is being kept updated, having sent his “fondest love and well-wishes” to his sister.
Buckingham Palace said the Princess was expected to make a “full and swift recovery”. She is expected to be discharged from hospital later this week.
A spokesman said she was “in a comfortable condition” and was being kept in hospital as a precautionary measure for further observation.
Rishi Sunak, the Prime Minister, and Sir Keir Starmer, the Labour leader, broke away from election campaigning to send the Princess their best wishes for a speedy recovery.
The Princess had been due to fly to Canada at the end of this week but has now postponed the trip on doctors’ advice. She sent her apologies to those who may be inconvenienced or disappointed as a result of her cancelled engagements.
She will also miss a state banquet held in honour of the Emperor and Empress of Japan’s visit on Tuesday evening.
It is not the first time that the Princess has lost her memory following an equestrian accident.
At the 1976 Olympics, she suffered a bad fall at a jump as her horse, Goodwill, became stuck in a boggy mud. She later described her memory as “almost non-existent for that day”.
The Princess, often dubbed the hardest-working member of the Royal family, is known for her no-nonsense approach and her commitment to royal duty.
At Trooping the Colour earlier this month, she was pictured expertly keeping her horse under control when it appeared agitated.