Nicola Hamman may be the first person in Britain to lose her job as a result of the new legislation introduced last week, which guarantees a statutory minimum wage of pounds 3.60 an hour and pounds 3 an hour to those under the age of 22.
Ms Hamman, who was paid pounds 50 for a 31-hour week, claims she was told to leave Crazy Cuts in Tirphil, Mid Glamorgan, after asking for her salary to be increased to pounds 93.
She says her employer, Karen Hill, then offered her a compromise whereby she would be paid pounds 93 a week if she worked an extra day for nothing.
Ms Hill claims she told Ms Hamman she could afford to keep her on at the minimum wage only if her hours were cut.
Ms Hamman said her working relationship with her boss of two months had been good before she asked for a wage rise.
"At first she told me I wasn't entitled to it because she was a small business. Then she said she couldn't afford to keep me on," she said. "I am fully qualified but all the other hairdressers I know are being paid the minimum wage, even if they are trainees.
"I feel really angry because I enjoyed my job and now I will have to sign on until I find something else. But there aren't many jobs around."
Ms Hill, denies offering to increase Ms Hamman's wages and said her employee left "of her own accord" before she had been able to discuss the reduction in her hours.
According to the regional youth organiser of the GMB union, Julia Rallings, an investigation is already under way and the incident could provide a test case for the new legislation, which is expected to benefit about two million people, if it goes to an industrial tribunal.
"It's an absolutely appalling case and it's important to make a stand," she said.
"We are encouraging young people to ask for their entitlement because some bosses of small businesses appear to be ignoring their responsibilities in the hope that their employees don't realise what is going on."