Boris Johnson had hinted at copying Scotland by introducing the rule, as he was pictured for the first time wearing a covering himself.
But, asked if that would be “mandatory” in shops, Mr Gove said. “I don’t think mandatory, but I would encourage people to wear face masks.
“It is basic good manners, courtesy and consideration to wear a face mask if, for example, you are in a shop. I trust people’s good sense.”
The cabinet office minister also revealed the government was significantly boosting the manufacture of face coverings, with factories “in Wales and Burnley”.
The government has been accused of spreading confusion on the issue, with only 36 per cent of Britons wearing coverings in public places – far short of the numbers in France (78 per cent) and Italy (83 per cent).
Some scientists had welcomed the prime minister’s hints at being ‘stricter”, when he said: “We are looking at ways of making sure that people really do have face coverings in shops, for instance, where there is a risk of transmission.”
Professor Venki Ramakrishnan, president of The Royal Society, said everyone’s mouth and nose should be covered in public, to reduce the risk of a second wave of coronavirus.
The World Health Organisation said last week that there is “emerging evidence” that infections could be spread through particles travelling through the air.
Speaking on the BBC’s The Andrew Marr Show, Mr Gove said “If tough measures are required, as we have seen in Leicester ... then tough measures will be taken.
“But on the whole, my view is it’s always best to trust people’s common sense, to give them a clear sense of what is wise.”
Mr Johnson finally wore a mask after Anthony Costello, a former director of the World Health Organisation, criticised the chancellor, Rishi Sunak, for failing to do so when serving customers to promote his meal-discount scheme.
Branding it “a terrible mistake”, the professor of global health said: “Our message is wear masks indoors, wear masks in public places – and ministers should be setting a good example.”
However, some epidemiologists are worried that masks are “a pretence to ease the lockdown to help the economy”.
And Mark Drakeford, the Welsh first minister, said he did not think the evidence on wearing face coverings was “decisive” yet.
But Rachel Reeves, the shadow cabinet office minister, said Labour backed the compulsory face coverings in shops as a “sensible way forward”.
“People want to do the right thing but they want to know what the right thing is. We already have it on public transport,” she said.
Mr Gove also confirmed the government wanted people to return to work, rather than stay at home, to ensure the “economic engines of this country are fired up again”.
“We want to see more people back at work, on the shop floor, in the office, wherever they can be,” he told Sky News.