The Chancellor of the Duchy of Lancaster had gone to Porto with his son to watch the Champions League final between Chelsea and Manchester City.
Mr Gove has been alerted through the NHS app that he may have been in contact with someone who had the virus on the flight home from Porto.
The Cabinet Office confirmed Mr Gove had been pinged by the app.
Mr Gove had been due to meet the first ministers of Scotland, Wales and Northern Ireland with the Prime Minister in a bid to strengthen the union.
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.