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” as the fabric used in manufacture had undergone extensive testing, quality control and trials.
“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.