The new all-Wales uniforms are designed to make it easier for patients to identify different grades of nurses.
A Welsh Assembly Government spokesman described the problems as disappointing because staff welfare was paramount.
The director of the Royal College of Nursing in Wales said it was essential that any problem was reported.
The uniforms are being rolled out by Hywel Dda Health Board, successor to Carmarthenshire Local Health Board, and Betsi Cadwaladr University Health Board in north Wales as part of an assembly government initiative.
Although the number of nurses who have reported skin irritation is "a minority", the assembly government said it was concerned because the welfare of staff was "paramount".
"As only a minority of staff have reported a problem, we have sufficient supplies of alternative uniforms for use," said a spokesman.
"We are also working in partnership with RCN [Royal College of Nursing] and UNISON [union] to address any concerns as quickly as possible."
He added that news of the problem was "disappointing"
"Robust testing of the fabric is currently being undertaken by an independent body to establish the exact nature of the problem and, throughout contractual arrangements, we expect the manufacturers to put this right," added the spokesman.
Occupational health
Tina Donnelly, director of the Royal College of Nursing in Wales, said that invariably when something such as a new uniform was introduced, there would be some people who developed a reaction.
She compared the introduction of the new uniform to when gloves were introduced to minimise infection.
"The gloves were there to stop cross infection, so all nurses were told to wear them, but some had a latex allergy," she said.
"Then those gloves were changed, and non-latex gloves with powder were introduced, and some people were allergic to the powder," she added.
It was important that people reported any problems to the occupational health department, and then if there was a significant problem the uniforms could be tested further, she said.
"We need staff feedback if there is a problem and I am happy with how it's being dealt with," she said.
Wales is the first nation in the UK to introduce a national uniform.
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