The prime minister said he was "pinged" by NHS Test and Trace on Sunday and told to self-isolate, but remains well.
Mr Johnson on Thursday spent about 35 minutes with Tory MP Lee Anderson, who lost his sense of taste the next day.
It comes as the government prepares a policy relaunch after fierce internal rows and departures from No 10.
Downing Street said a series of "critical announcements" would this week detail Mr Johnson's "ambitions for the United Kingdom".
They follow the dramztic departure of the PM 's chief adviser Dominic Cummings last week.
Mr Johnson will chair "key Covid meetings" and work with Chancellor Rishi Sunak to devise the upcoming spending review with an aim to fulfil his promise to "build back better".
The PM will now be working from his flat at Downing Street.
On Thursday, Mr Anderson, the Conservative MP for Ashfield, posted a photo of himself with Mr Johnson at No 10 alongside the words: "Breakfast with the PM."
On Sunday, he posted on his Facebook page to say he was self-isolating with his wife, who is clinically vulnerable, after they both tested positive.