The Countess of Chester NHS Foundation Trust decision will impact on thousands of people in Flintshire who currently use it, with immediate effect.
The decision follows a row over payments to the hospital for caring for patients from Wales.
A Welsh Government spokesman said limiting access to Wales' patients on financial grounds was "not acceptable".
GPs in Wales will no longer be able to refer patients for treatment over the border at the hospital.
Wrexham Maelor Hospital and Ysbyty Glan Clwyd are the next closest hospitals for patients in the area.
Chief executive of Countess of Chester Hospital, Susan Gilby, said it was
"a difficult decision" down to "unresolved funding issues"."Unfortunately, the trust is currently unable to accept any new elective work relating to patients living in Wales.
"We will of course honour any existing appointments so there will be no disruption for patients already waiting.
"This is a difficult decision that has been taken with great reluctance.
Ms Gilby added that contract negotiations were continuing and the trust was working with Betsi Cadwaladr University Health Board in north Wales to resolve the issue.The trust's chairman, Sir Duncan Nichol, previously said caring for patients from Wales was "hard to countenance" due to costs.The trust told BBC Wales in October 2018 that 23,500 patients from Wales were treated over the border in 2016-17 for mainly secondary care, which cost £31.2m.
Evan Moore, from Betsi Cadwaladr, said they were working to "accommodate newly referred patients" within existing services in Wales.
"We will be writing to all affected GPs and medical staff to inform them of these changes," he said.
Mr Moore added that the decision did not affect cancer patients, urgent elective patients already referred to COC
Speaking at a Welsh Assembly scrutiny committee, Mark Drakeford said if the Countess of Chester did not provide services then it will "have to face up to facts"
that funding from Wales "is not going to flow to them in future"."There is a very direct interest that they have at stake here, which they sometimes, seems to me, underplay in the public statements that they make," he said.Mr Drakeford said the immediate focus in resolving the problem should be via a "sensible agreement" between both sides.
"Welsh patients are part of their bottom line, in the way that the English system is run."
"Some sense of reciprocity is essential in all of this - and reciprocity from the Countess of Chester needs to be part of that conversation," he said.
"Over the period of devolution, there are regular suggestions from English providers that sometimes Wales doesn't pay our bills.
"Every time that has been looked at that, that has turned out not to be true. We have always paid our bills."
Speaking to BBC Radio Wales, Wrexham-based GP Dr Peter Saul said:
"They [both sides] should have reached an agreement and they certainly shouldn't have put patients at risk."They shouldn't be taking unilateral action, they need to get back together and sort this out.Dr Eamonn Jessup, a locum GP in north Wales added: "North Wales does not have enough capacity for the demand upon it as it is, a sudden influx of patients like this will cause the service to collapse."
"One of the problems that is already happening is that if we can't send patients to hospitals that have traditionally taken them, it puts an additional strain on hospitals on the Welsh side of the border and they are already struggling with capacity."
The Robert Jones and Agnes Hunt Orthopaedic Hospital NHS Foundation Trust, in Gobowen, Shropshire, said it had no current funding issues with the Welsh Government.
But it added it was "aware of a potential issue emerging for the forthcoming year that we understand is being discussed between the Department of Health and Welsh Government".
Shrewsbury and Telford Hospital NHS Trust, which is the main provider of general hospital services for Shropshire, Telford & Wrekin and mid-Wales, said it was not affected.
There will and should be cross boarder cooperation between counties when it comes to health provision , and I see no reason even with different health policies an Independent Wales could not work out to catty on doing so with our English neighbours.
But we need to ask the question ,why does it seem to be going only one way ?
Twenty years after devolution there has seemed to be little move to address the issue by providing health care for those who are affected and face crossing the boarder to seek the care they need.
Even without devolution it would be very likely that such a row between different Health Authorities , would occasionally develop.
On Tuesday I have to attend a clinic at the Heath Hospital in Cardiff at my last one I met a woman with the same condition who had travelled from Carmarthen, and I believe it deals with people from Pembrokeshire. So a number of different Health Authorities, will face paying for treatment i another.
Its not just a question of Welsh Identity, its about making sure patients do not have to travel long distances.
Maybe we should consider building an hospital that accommodate people , who face the dilemma of crossing the boarder , for the health care they need.
Certainly we can't carry on with English NHS hospitals treating Welsh Patients as second class citizens even if they are paying the same as their counterparts on that side of the boarder.