"She will continue to receive medical attention and will follow all the appropriate guidelines," the palace said in a statement.
People in the UK who test positive for Covid are required to self-isolate for at least five days, although the British government says it plans to lift that requirement for England this week.
Both the Queen's eldest son Prince Charles, 73, and her 74-year-old daughter-in-law Camilla, Duchess of Cornwall contracted Covid-19 earlier this month. Charles has since returned to work. There are also thought to be several recent virus cases among staff at Windsor Castle, where the Queen is staying.
A host of senior British politicians sent get-well messages. Prime Minister Boris Johnson tweeted: "I'm sure I speak for everyone in wishing Her Majesty The Queen a swift recovery from Covid and a rapid return to vibrant good health."
Health Secretary Sajid Javid wrote that he was "Wishing Her Majesty The Queen a quick recovery," while opposition Labour Party leader Keir Starmer wished the Queen "good health and a speedy recovery. Get well soon, Ma'am."
Elizabeth has been in robust health for most of her reign and has been photographed riding a horse as recently as 2020. In the past year she has been seen using a walking stick, and in October she spent a night in a London hospital for unspecified tests.
The Queen's doctors ordered her to rest after that and she was forced to cancel appearances at several key events, including Remembrance Sunday services and the COP26 climate conference in Glasgow, Scotland in November.
This month she returned to public duties and has held audiences both virtually and in person with diplomats, politicians and senior military officers. During one exchange caught on camera last week, she walked slowly with a stick and said "as you can see I can't move" in apparent reference to her leg.
Joe Little, managing editor of Majesty magazine, said members of the royal family would be very concerned by the Covid-19 diagnosis.
"I would guess that she will be matter-of-fact about the diagnosis in a way perhaps that the people around her are less matter-of-fact," he said.
The Queen has a busy schedule over the next few months of her Platinum Jubilee year, and is scheduled to attend in-person public engagements in the coming weeks, including a diplomatic reception at Windsor on March 2 and the Commonwealth Service at Westminster Abbey on March 14.
On March 29, she has a remembrance service at Westminster Abbey for her husband Prince Philip, who died in April 2021 at 99.
Public celebrations of the Platinum Jubilee are scheduled over a long weekend June 2-5, with festivities including a military parade, a day of horse racing and neighbourhood parties.
The Queen is the latest monarch from around the world to catch Covid-19. Queen Margrethe of Denmark, 82, and Spain's King Felipe VI, 54, both tested positive for the illness earlier in February and had mild symptoms.
Her diagnosis comes after a difficult week for Britain's royal family.
On Tuesday the Queen's second son, Prince Andrew, settled a US lawsuit brought by a woman who claimed he had sexually abused with her when she was 17 and travelling with the late financier and sex offender Jeffrey Epstein. Andrew strenuously denied the claim by Virginia Giuffre. He agreed in a settlement to make a substantial donation to his accuser's charity.
On Wednesday, London's Metropolitan Police launched an investigation into allegations that people associated with one of Prince Charles' charities offered to help a Saudi billionaire secure honours and citizenship in return for donations.
