The approach is in contrast to England’s road map out of lockdown, where Prime Minister Boris Johnson has said the legal obligation to wear face coverings will end once the country reaches Step 4 on July 19.
A final decision on England’s path out of restrictions is due to be taken on Monday.
However, in Wales masks must still be worn in taxis, on trains and buses, as well as health and social care settings when coronavirus restrictions are eased, the Welsh Government said.
Keeping everyone safe has been the Welsh Government’s priority through the pandemic and will continue to be the priority in future
Welsh Health Minister Eluned Morgan
It added that “active further consideration” is being given to whether they will still be required by law in other settings, like retail.
First Minister Mark Drakeford said: “We will need everyone’s help to keep coronavirus under control as we continue to respond to the pandemic – this virus has quite certainly not gone away.
“We know many people are still worried and anxious about going out. We will maintain the requirement to wear face coverings in certain places – on public transport and health and social care settings, and others where necessary – to help keep us all safe.”
Making the announcement on Sunday, the government said scientific evidence supports the use of face coverings as a way of reducing the transmission of the virus.
It said they are “particularly useful” in crowded, indoor areas with poor ventilation.
Health Minister Eluned Morgan said: “Wearing face masks is an effective way of reducing the transmission of coronavirus.
“We all have a duty to help to protect each other. Keeping everyone safe has been the Welsh Government’s priority through the pandemic and will continue to be the priority in future.”
On Friday, it was announced that face coverings will not be routinely recommended in classrooms across Wales from September.
Mr Drakeford is expected to make a statement on Wednesday setting out further details on the new alert level zero for Wales.
The country is currently at alert level one and face coverings are mandatory in all indoor public places.
Scottish First Minister Nicola Sturgeon is due to announce her country’s next steps out of lockdown in a statement to the Scottish Parliament on Tuesday, but has already described Mr Johnson’s approach as “something of an exception”, appearing to indicate hers will be more cautious.
In Northern Ireland, the removal of rules around all face coverings, with regulations potentially replaced by guidance, are due to be considered next month.
The Stormont Executive has already announced that the legal requirement to wear face coverings in places of worship is also set to be removed on July 26, while the use of face masks in classrooms is to be removed from guidance.