New measures mean migrants from outside Europe must be earning £35,000 or more to stay in the UK after six years.
It's thought around 3,365 nurses currently working in the UK will have to leave the country because of the change which Steve Fouch told Premier would be a 'problem'.
The average salary of a nurse in the UK is around £23,000 a year which the Royal College of Nursing (RCN) said would mean many NHS staff will be caught out by the rules.
Steve Fouch told Premier the NHS was struggling to recruit staff from the UK and so had been forced to turn to countries overseas.
"These new regulations that are coming in mean that a significant number of them, because they're on quite low pay, will not qualify to stay in the county.
"This means we could be seeing thousands of relatively low paid nurses leaving the country at a time when we're struggling to find enough nursing staff to run things at the NHS as it is.
"And of course we're also talking about an increase to a seven day a week NHS which is going to need more staff so it's a problem."
A Home Office spokesman said: "As the Prime Minister has made clear, the Government wants to reduce the demand for migrant labour.
"We changed the settlement rules in 2011 to break the link between coming to work in the UK and staying here permanently. From 2016, non-EEA workers will need to earn at least £35,000 to settle in the UK for longer than six years.
"There are exemptions to this threshold for occupations where the UK has a shortage - but the independent Migration Advisory Committee recommended against adding nurses to the Shortage Occupation List after taking evidence from groups including the Royal College of Nursing.
"Employers have had since 2011 to prepare for the possibility their non-EEA workers may not meet the required salary threshold to remain in the UK permanently."
Premier's Antony Bushfield speaking to Steve Fouch:
