The programme heard calls for vets’ part in the system to be investigated.
Minister Rebecca Evans told AMs the “horror and anger” prompted by the programme was shared by the Welsh Government.
She said Rural Affairs Minister Lesley Griffiths would instigate a review of the current breeding regulations, write to veterinary bodies and local councils about the issue and also discuss the matter with Chief Veterinary Officer for Wales Christianne Glossop on Wednesday.
As part of the licensing process breeders pay vets to check dogs to decide if they’re “fit to breed”. An expert panel told the programme, broadcast on Monday night, that some vets’ standards had “slipped” and they were “part of” a “broken system”.
Welsh Government regulations mean anyone who breeds three litters or more per year must be licensed by their local council.
The investigation visited many approved sites and found dogs suffering from infections and kept in poor conditions with little access to exercise.
In annual health checks seen by the BBC, vets also recorded significant numbers of dogs with serious health conditions at approved sites, but breeders were allowed to continue operating, year after year.
Ms Evans made her comments responding to a question from the Labour assembly member Joyce Watson, who said there had been “an absolute failure of duty from vets” and the programme had shown “cruelty beyond belief in council registered puppy farms”.
“It showed hundreds of dogs living in filthy, dark, damp and cold conditions,” Ms Watson said.
“These premises are inspected annually by inspectors and vets, people who are supposed to prioritise the welfare of the animals.”
Ms Evans replied: “Obviously, we share her sense of horror, but also, her anger, at what she has seen happening here in Wales, where we’re supposed to be a nation of animal lovers, but then, we see things like this happening.
“I know that the minister for environment and rural affairs has, or intends to very shortly, written to veterinary bodies, and also, to local authorities about this specific issue.
“She’s meeting he chief veterinary officer tomorrow, but I also know that the minister intends to ask the animal welfare framework group to revisit the current breeding regulations to improve welfare conditions at breeding establishments.”