A Welsh government spokesperson said they were "very disappointed that nursing courses form part of these proposals" and that it was "working urgently" to ensure the same number of nurses are trained in Wales.
They said they understood "the serious concern" the announcement will cause.
"Universities across the UK are facing a challenging financial period due to a range of factors and we expect all institutions to work with trade unions, staff and students on any proposals," they added.
The Royal College of Nursing said the proposal to shut the school of nursing "has the potential to threaten the pipeline of registered nurses into the largest health board in Wales".
Ruth Jones MP, Chair of the Welsh Affairs Committee, compared the job cuts to a "canary in a coalmine" for the severe financial pressures facing universities across the UK.
"It is not only academics and students who will suffer from these cuts, but the wider community in south Wales," Ms Jones added.
Conservative Senedd member Natasha Asghar MS, said she feared "that these concerns will be repeated across our universities in Wales".
Plaid Cymru's education spokesperson, Cefin Campbell MS said the job losses would have "a devastating impact", damaging Wales' "reputation as a nation of learning".
Madison Hutchinson, Cardiff University Student Union president, said they "want to express our unwavering support with all students, and solidarity to staff who may be impacted".
"We have had a commitment from the university that all impacted students will be communicated with tomorrow," she added.