The Apprenticeship Pay Survey, published by the Department of Business, Innovation and Skills, showed the number of apprentices paid below the minimum wage increased by 45% in 2012.
The study showed 29% did not receive the then legal minimum of £2.65 per hour last year, up from 20% the year before. This month, the legal minimum wage for apprentices increased to £2.68 per hour.
TUC general secretary Frances O'Grady called the findings "shocking".
"Apprentice exploitation is getting worse across the board. In some industries, such as hairdressing, abuse has become endemic. Ministers must launch investigations now into this abuse," O'Grady said.
"There are plenty of bad bosses who have deliberately cheated young workers. And it appears many businesses do not understand how minimum wage rates work.
"Unless the Government does more to make companies aware of their responsibilities, as well as naming, shaming and persecuting rogue employers, many apprentices will continue to be exploited."
'Close the gap'
In its submission to the Low Pay Commission, the TUC has called for the current apprenticeship rate of £2.68 an hour to rise significantly, and for the gap with the 16-17 year-old minimum wage youth rate (£3.72) to close.
The study found the worst industry for paying minimum wage was hairdressing, where 69% of apprentices were paid less than the legal minimum in 2012. Other underpaying industries were childcare (53%) and construction (42%).
Skills minister Matthew Hancock said that creating the right pay and working conditions for apprentices was crucial to the continued success of the programme.
"I am very clear about the importance of the national minimum wage," he said. "Paying less than the minimum wage is illegal and if employers break this law they need to know that we will take action.
"We have revised the national minimum wage naming scheme, so it is easier to name and shame employers who break minimum wage law, alongside increasing awareness of the minimum wage rules and ensuring all training providers inform employers and apprentices of the requirements."
Last week, the Government announced the minimum wage for adults increased by 12p to £6.31 an hour, and by 5p to £5.03 an hour for 18 to 20 year-olds.
The minimum wage for 16 and 17 year-olds will receive has risen by 4p to £3.72, while the apprentice rate goes up by 3p to £2.68.