Kate was due to spend the day with William celebrating the 73rd anniversary of the NHS at two major events but will now have a 10-day period at home.
They had planned to attend a Service of Thanksgiving at St Paul's Cathedral in honour of the nation's health service, and in the afternoon host a Big Tea at Buckingham Palace for NHS staff, in their roles as Joint Patrons of NHS Charities Together.
Kensington Palace said in a statement: "Last week The Duchess of Cambridge came into contact with someone who has subsequently tested positive for Covid-19.
"Her Royal Highness is not experiencing any symptoms, but is following all relevant government guidelines and is self-isolating at home."
Kate's last public event was a visit to Wimbledon on Friday when she toured the SW19 sporting venue meeting staff in the museum, Centre Court kitchen and sitting to watch Jamie Murray play in the doubles.
The duchess is patron of the All England Lawn Tennis Club and a keen tennis fan but is now likely to miss the men's and Women's final at the weekend.
William contracted Covid last spring and was able to carry on with telephone and online engagements while he was treated by royal doctors but was reportedly hit "pretty hard" by the virus and at one stage struggled to breathe.
The Prince of Wales also caught the virus during the same period but had milder symptoms although he did lose his sense of smell and taste for a period.