A hospital trust official emailed mid Wales politicians to say it had failed to recruit foreign nurses because it could not get Home Office approval.
Nursing is not on the Shortage Occupation List, giving priority to migrants with specific qualifications.
UK ministers said they took independent advice on the list and the long-term aim was to "train our own nurses".
Health Minister Mark Drakeford said: "We have argued in favour of including nursing on the list. It seems essential to me.
It is just a wrongheaded focus on the wrong issue that is leading them to refuse to do that. I've argued as well for a separate Welsh Shortage Occupation List."
Shrewsbury and Telford Hospital Trust, which serves mid Wales patients, could not recruit the nurses because it had been unable to get certificates of sponsorship from the Home Office, according to the email.
Trust Communications director Adrian Osborne sent the message to MPs and AMs in mid Wales, Shropshire and Telford & Wrekin.
He wrote: "Alongside our local recruitment and training programmes, we had also implemented an international recruitment programme focused on the Philippines.
"This has faced delays as we have not been successful in securing Certificates of Sponsorship from the Home Office to bring these nurses to our wards.
"This is because nursing is neither on the Shortage Occupation List, nor do these posts secure enough points for them to be a priority for the Migration Advisory Committee."
Lib Dem AM William Powell has written to the UK government calling for a change to the policy.
"The Tories' irresponsible and illogical attitude to immigration is contributing to an NHS staffing crisis in Wales," he said.
"What kind of government wants to stop vitally needed nurses coming to work in our country?  This is reckless in the extreme.
"Of course we need to be training nurses in this country and we need a clear strategy to train our workforce for the future, but patients need support now, not in ten years' time."
In a letter to Mr Powell, Immigration Minister James Brokenshire said: "The UK government believes that in the past it has been too easy for employers to bring in workers from overseas rather than take the long-term decision to train our workforce here at home.
"The long-term aim is that we train our own nurses in this country.
"A number of health professional jobs, such as doctors in emergency medicine, are recognised shortage occupations, but the Migration Advisory Committee (MAC) recently recommended against adding nurses to the Shortage Occupation List."
The UK government's immigration policy is contributing to an NHS staff crisis, the Welsh Liberal Democrats have said.