It said a lack of funding and rising costs meant many could struggle to stay afloat.
Thirty hours of free care for three and four year olds was one of Labour's flagship pledges at the 2016 elections.
The Welsh Government said private provision will play a central role in delivering the policy.
It said the policy would be based on properly worked out pilot schemes.
A survey by the association of mostly private nurseries found almost half were uncertain or unlikely to offer the government's policy because they worried Welsh Government funding will not cover the costs.
About one in five nurseries - a total of 122 - in Wales took part in the association's survey.
Association chief executive Purnima Tanuku said: "Nurseries really want to be able to offer families the help with funded childcare that the government is promising them.
"But they cannot do this if accepting children for 30 'free' hours causes them to make a loss that could put them out of business."
Darren Millar, Welsh Conservative spokesman on children, said the findings cast "serious doubt over the Welsh Labour Government's ability to fulfil its manifesto commitment to deliver free childcare".
"It's clear that the nurseries across the sector are suffering from inadequate levels of funding and Labour ministers' poor handling of the new business rates revaluation, with many providers running to a significant annual loss as a consequence," he said.
A spokesman for Communities Secretary Carl Sargeant said: "When implemented, Welsh Labour's childcare offer will be the best in the UK for working parents.
"Unlike the Tory government in England, which has jumped into hasty and widely criticised implementation of its childcare scheme, we are proceeding on the basis of careful consultation and properly worked out pilots ensuring that our scheme works effectively for parents from day one.
"Private provision will play a central role in delivering our offer.
"Childcare providers in Wales are entitled to an enhanced level of support through our £100m Small Business Rates Relief Scheme.
"We have also announced an extra £20m of support for small businesses in 2017-18 through two bespoke schemes, including a transitional support scheme."
Thousands of parents may struggle to get the free childcare promised by the Welsh Government, according to the National Day Nurseries Association.