The palace said the monarch is experiencing “mild cold-like symptoms” but expects to continue “light duties” at Windsor over the coming week.
“She will continue to receive medical attention and will follow all the appropriate guidelines,” the palace said in a statement.
The Queen, 95, had been in contact with her eldest son and heir, the Prince of Wales, who tested positive last week.
The announcement comes weeks after the Queen became the UK’s longest reigning monarch, reaching her Platinum Jubilee of 70 years on 6 February.
She carried out her first major public engagement for more than three months on the eve of her Jubilee, meeting charity workers at Sandringham House.
BBC royal correspondent Nicholas Witchell said it can be taken as absolutely certain that the Queen is fully vaccinated.