It is not known which member of his family has tested positive but he lives with his wife, Carrie Johnson, and his two children, Wilfred, 20 months, and Romy, who is five weeks old.
However, ministers have thrown their support behind him, with Northern Ireland Secretary Brandon Lewis backing Mr Johnson to lead the party into the next election and to win it.
“That is making a pre-judgement on what the report will find,” he told Kay Burley.
But, asked if Mr Johnson can continue as prime minister if an investigation finds he misled parliament by insisting he did not break COVID rules – in theory a resigning matter – Mr Lewis dodged the question.
A Number 10 spokesman said the prime minister will “follow the guidance for vaccinated close contacts, including daily testing and limiting contact with others”.
The visit cancellation comes a day after Mr Johnson apologised for attending a party at Number 10 during the first lockdown, which has prompted calls for his resignation from the opposition but also from within his own party.