Alok Sharma said businesses would need to comply with social distancing rules, and said restaurants, pubs, bars and hairdressers would still need to wait until at least July 4 to open their doors.
But he said from June 15, other shops can welcome customers back.
He said: “This is the latest step in the careful restarting of our economy and will enable high streets up and down the country to spring back to life.”
Enforcement notices can be issued if shops reopen without following the guidance, he added.
Mr Sharma said: “Of course, there are businesses which still remain closed. As soon as we can we will publish further safer working guidance for restaurants, pubs and bars, as well as hairdressers, barbers, nail bars and related services.
“I know there’s been a lot of speculation about when we might be able to reopen these parts of the economy and I completely understand why we’re all so keen to get them back up and running, and I absolutely share that enthusiasm.
“But we continue to follow the road map which set out our ambition to reopen these sectors from July 4 at the earliest.”
He also said the Government was keeping the two-metre social distancing rule, which has been of concern to the hospitality industry, under review.
“When it is safe to do so, we will see whether you can move to a shorter distance but ultimately we keep all of these things under review,” he told the No 10 briefing.
“There are other countries in the world that have moved from two metres to closer distances. Of course, they are further along in terms of their road map, in terms of opening up businesses.
“We are taking a cautious view on this. I completely understand why for economic reasons businesses will want to have a look at this two-metre rule.”
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