First Minister Mark Drakeford has described stopping supermarkets from selling non-essential products during the firebreak lockdown as "a straightforward matter of fairness".
Mr Drakeford said the Welsh Government had been clear that non-essential retail would close during the 17-day period, which begins at 6pm on Friday.
He told a press conference in Cardiff that any suggestion that the ban, which was announced on Thursday, was based on his own politics was "nonsensical".
He said this would ensure a "level playing field" as many retailers will be forced to shut when the 17-day lockdown begins on Friday.
Shops selling food, off-licences and pharmacies can stay open but the likes of clothes stores will have to close.
Mr Drakeford made the announcement at a Senedd committee in response to a question from Conservative MS Russell George who said it was "unfair" to force independent clothing and hardware retailers to close while similar goods were on sale in major supermarkets.
"In the first set of restrictions people were reasonably understanding of the fact that supermarkets didn't close all the things that they may have needed to," Mr Drakeford said.
"I don't think that people will be as understanding this time and we will be making it clear to supermarkets that they are only able to open those parts of their business that provide essential goods to people and that will not include some of the things that Russell George mentioned which other people are prevented from selling.
"So, we will make sure there is a more level playing field in those next two weeks."
From Friday all leisure and non-essential retail will be closed and this includes clothes shops, furniture shops and car dealerships.
Shops allowed to remain open include supermarkets and other food retailers, pharmacies, banks and post offices.
Under the law, firms conducting a business that provides a mixed set of services will be allowed to open if they cease conducting the service that must close.
The Welsh Conservatives called for urgent clarity on what items are considered to be essential, while supermarkets said staff were working hard to comply with the restriction.
On Friday afternoon, the Welsh Government issued guidance stating that certain sections or aisles of large supermarkets or department stores "must be cordoned off or emptied, and closed to the public".
These include areas selling electrical goods, telephones, clothes, toys and games, and products for the garden, as well as a dedicated section for homeware products.
Supplies for the "essential upkeep, maintenance and functioning of the household" - such as batteries, lightbulbs and rubber gloves - can be sold during the lockdown.
Andrew RT Davies, the Conservative shadow health minister, tweeted: "The power is going to their heads."
He later added: "Is a flagon of Strongbow deemed essential? What about some much-needed underpants if you're caught short?
"I do hope there is some published guidance on what the Labour commissars deem as essential."
Sue Davies, from consumer group Which?, said the announcement would cause "confusion", particularly among the vulnerable.
Mr Drakeford said: "We are requiring many hundreds of small businesses to close on the high street right across Wales.
"We cannot do that and then allow supermarkets to sell goods that those people are unable to sell.
"And we are looking to minimise the amount of time that people spend out of their homes during this two-week period.
"This is not the time to be browsing around supermarkets looking for non-essential goods."
Mr Drakeford said trying to find exceptions to the rules was "just the wrong" approach and called on people in Wales to not use the firebreak to do things that they do not have to.
"It is a straightforward matter of fairness - we are in this together here in Wales," Mr Drakeford said.
A Sainsbury's spokesman said staff had been working "around the clock" to put the necessary changes in place.
"We're focused on providing our customers with food and other essential items, in line with government guidance," he said.
Waitrose told PA that it was reviewing the Welsh Government's guidance and "working through what this means for our business".
Tesco said staff were working "incredibly hard" to ensure stores complied with the Welsh Government's ban on selling non-essential goods.
Asda confirmed the regulations meant that only products deemed essential could be sold during the lockdown.
"We have been given very little time to implement these changes or clarity on what is deemed 'essential'," a spokesman said.
"We have expressed our deep concerns about the implications for customers accessing products they genuinely need and the risk to our colleagues safety."