Buckingham Palace said changes were being made to the Queen's diary commitments "as a sensible precaution".
She was due to visit Crewe and Macclesfield in Cheshire on 19 March and Camden on 26 March.
It comes after the Prince of Wales and Duchess of Cornwall postponed their spring tour of Bosnia and Herzegovina, Cyprus, and Jordan due to the pandemic.
There have been 798 confirmed cases of coronavirus across the UK - as of Friday morning - and more than 125,000 globally.
In total, 10 people have now died in the UK as a result of the virus.
A spokesman for the Queen said her diary would be adjusted in the coming weeks "for practical reasons in the current circumstances".
"Audiences will continue as usual," a statement added. "Other events will be reviewed on an ongoing basis in line with the appropriate advice."
Next Thursday's day of engagements would have seen the monarch, 93, travel to Cheshire to meet staff and apprentices at the Bentley car factory, operate the Lovell Telescope at the Jodrell Bank observatory and meet local school children engaging in hands-on science activities.
It comes after the Queen wore gloves when she handed out honours to recipients at a Buckingham Palace investiture on 3 March.
She has since attended the Commonwealth Service at Westminster Abbey and held one-to-one audiences at Buckingham Palace.
Meanwhile, Prince Charles and Camilla have postponed a tour of Bosnia and Herzegovina, Cyprus and Jordan - due to begin in four days' time. It was to be the first official royal visit to Cyprus for 27 years.
A spokesman for Clarence House said on Friday that the decision was taken "owing to the unfolding situation with the coronavirus pandemic".
Prince Charles was preparing to travel to Bosnia and Herzegovina on Tuesday, and was to be joined by Camilla in Cyprus from Wednesday, before the couple would travel together to Jordan until 25 March.
The prince's solo visit to Bosnia and Herzegovina was for him to pay his respects as the country marks the 25th anniversary of the Srebrenica genocide.
The trip may be replaced with engagements in the UK - but not involving significant gatherings of people to avoid any extra strain on public services.
I knew that if I failed I wouldn’t regret that, but I knew the one thing I might regret is not trying.