She had been due to spend the day with the Duke of Cambridge to mark the 73rd anniversary of the NHS.
But Prince William arrived alone for a service at St Paul's Cathedral and a Buckingham Palace tea for NHS staff.
Kensington Palace said she does not have any symptoms, but is "following all relevant government guidelines".
It said in a statement: "Last week the Duchess of Cambridge came into contact with someone who has subsequently tested positive for COVID-19.