It follows a similar scandal at fashion brand Boohoo, which appointed a QC to investigate the allegations last week.
Quiz chief executive Tarak Ramzan said: “We are extremely concerned and disappointed to be informed of the alleged breach of national living wage requirements in a factory making Quiz products.
“The alleged breaches to both the law and Quiz’s ethical code of practice are totally unacceptable.
“We are thoroughly investigating this incident and will also conduct a fuller review of our supplier auditing processes to ensure that they are robust. We will update our stakeholders in due course.”