Michael Gove had to abandon a meeting with Boris Johnson and devolved leaders after he was alerted by the NHS test and trace app.
The Chancellor of the Duchy of Lancaster was pinged by the coronavirus app that he had come into contact with somebody who had tested positive recently.
It is understood to have happened as he flew back to the UK after attending the Champions League final in Portugal with his son last weekend.
Instead of self-isolating for 10 days, Mr Gove will be able to take part in a pilot scheme for workplaces, where he can instead be tested every day for a week.
Returning football fans have been told to self-isolate after some flights reported passengers testing positive for Covid.
Posting on a fan forum, passengers reported as many as five flights organised by Manchester City for the match against Chelsea had been affected.
Mr Gove was in the middle of a meeting with the PM, Chancellor Rishi Sunak, other ministers and the leaders of devolved administrations when he got the notification.
Scotland’s First Minister Nicola Sturgeon, Welsh First Minister Mark Drakeford and Northern Ireland’s leader Arlene Foster were all taking part remotely in the meeting on recovery from the pandemic.
A spokesman for Mr Gove said: “The Chancellor of the Duchy of Lancaster is participating in the daily contact testing programme after being advised to isolate today by NHS Test and Trace.
“He has followed COVID-19 regulations and guidance at all times and will continue to do so.”
But shadow sports minister Alison McGovern said it was unfair that Mr Gove will not have to self-isolate in the same way as ordinary fans who may also have received an alert.
Ms McGovern said: “Doesn’t that sound like one rule for him and one rule for everybody else?”
Good Morning Britain presenter Richard Madeley asked Communities Secretary Robert Jenrick: “Forgive my cynicism, but you talk about caution – how is it that your Cabinet colleague Mr Gove has been pinged on track and trace and yet, like the rest of us, he doesn’t have to isolate, he’s just doing tests?”
Mr Jenrick said: “I haven’t spoken to Michael so I don’t know all the details exactly but it sounds like the system worked. He’s taking part in a pilot, as I understand, where people can have slightly different circumstances.
“But I’m sure he’s going to take all of the necessary precautions, he’s not been coming into the office.”
About 12,000 football fans made the trip to Porto for the final, with each team allocated half of the figure in match tickets.
Dom Farrell, a sports journalist for Stats Perform, travelled to Porto for work and received a notification from NHS Test and Trace four days after flying home, telling him he needed to self-isolate for seven days.
He said a colleague on the same flight had received the same notification, leading him to believe that others onboard had too.
Andy Saunders, from St Albans, was told by his NHS Test and Trace app to self-isolate for 10 days after returning on a flight from Chelsea’s “appointed travel partner” – a Tui flight, he said.