Matt Hancock will self-isolate until the end of the week after receiving a test and trace alert on the NHS app.
In a video message the health secretary said complying with notifications on the app was “perhaps the most important part of all social distancing” regulations.
Mr Hancock said he would work from home until Sunday.
“Last night I was pinged by the NHS coronavirus app, so that means I’ll be self-isolating at home, not leaving the house at all until Sunday,” he explained.
“This self-isolation is perhaps the most important part of all the social distancing because I know from the app I’ve been in close contact with somebody who has tested positive and this is how we break the chains of transmission.
“So you must follow these rules like I’m going to. I’ve got to work from home for the next six days, and together, by doing this, by following this, and all the other panoply of rules that we've had to put in place, we can get through this and beat this virus.”
Former chancellor George Osborne questioned why ministers like Mr Hancock were not high on the list for vaccinations so they can continue to lead the fight against Covid-19 without fear of becoming sick with the disease.
“It’s a peculiarly British trait that we rightly make vaccinating millions of health workers a priority, but we can’t spare a single dose for the health secretary leading the response to the pandemic,” said Mr Osborne.
But Boris Johnson’s official spokesperson rejected the idea, telling reporters: “The prime minister and the rest of the cabinet will take the vaccine when it is their turn to do so, based on the priority lists that have been published.
“We don’t think it is right that the prime minister or other members of cabinet take the vaccine in place of somebody who is at higher clinical risk.”
Asked whether Mr Hancock could be sure that the app alert was not a false alarm, the spokesperson said: “We have been clear that if you are contacted by NHS Test and Trace, whether by phone, through the app or by email we are asking everybody to abide by their instruction to isolate.
“What you are seeing is Matt Hancock abiding by test and trace’s request for him to isolate.”
The spokesperson made clear that Downing Street was not concerned about the weekend’s photographs of the health secretary playing rugby with his son in a park, saying: “People are allowed outside to exercise, which is what I believe Matt Hancock was doing.”
The NHS contact tracing app was released in September. It allows people to report their symptoms and Covid-19 test results, and monitors whether users come into contact with anyone else using the app who has tested positive.
Mr Hancock’s isolation comes as new figures from the ONS show an estimated one in eight people in England had had Covid-19 by December last year – up from one in 11 in November.