It follows images of people socialising in the sunshine over the weekend.
Both the Prime Minister and Wales' First Minister have warned further measures will be introduced if people don't listen to advice on social distancing.
Concern has been raised after crowds of people were seen on beaches and at beauty spots across the country.
Pictures on social media show people climbing Pen Y Fan and Snowdon as well as congregating on the sea fronts at Porthcawl, Mumbles and Llanelli and on Gower's beaches.
Many weren't observing the 2 metre distance needed to prevent the spread of Covid 19.
A statement has been released on behalf of Mark Drakeford:
"Self-isolation for those who have symptoms and social distancing by everyone is absolutely essential at this stage if we are to delay the spread of this virus and save lives.
"We all need to follow this advice now to protect each other and our families and to help ensure our NHS is not overwhelmed.
"Social distancing includes avoiding all but essential travel and if people don’t follow this advice we will have no choice but to use powers to enforce it."
Llanelli AM Lee Waters has also taken to Twitter raising his concerns about the number of people ignoring social distancing advice.
THIS IS NOT A NORMAL SUNDAY! pic.twitter.com/mKP4hjrTTX— Lee Waters AM (@Amanwy) March 22, 2020
Here in Wales, we've seen a rise of 71 new cases of Covid 19 - bringing the total number of cases here to 347.
12 people have died.
Across the UK, there have been just over 5 and a half thousand confirmed cases with 281 deaths.
Letters are being sent to 70 thousand of Wales' most vulnerable people advising them to stay indoors for the next few months in order to protect themselves from Covid 19.
It's as parents across Wales are being reminded that most children should be at home - not at school - this week.
Limited places are available for certain children - like those who's parents are NHS workers - but the vast majority should be at home to avoid spreading the virus.
Swansea is the latest council to close playgrounds in a bid to stop the spread of Covid 19.
Similar moves were announced by Carmarthenshire and Neath Port Talbot councils over the weekend.
Larger, country parks like Margam and Pembrey have also been closed.