A number of employers who paid staff less than the minimum wage will have to pay a total of more than £20,000.
A list published by the UK government showed 14 Welsh businesses had underpaid a total of 64 workers – with some being owed more than £1,000.
But a Michelin-starred chef said it was “disgusting” the UK government had “named and shamed” his restaurant.
The government said companies have 14 days to make “representations” before they are named.
Restaurant James Sommerin, in Penarth, Vale of Glamorgan, is one of 14 Welsh companies on the list after failing to pay one employee £487.
James and Louise Sommerin, who run the business, said in a statement: “It’s disgusting that the government can name and shame like this as in our case a genuine mistake was made.
“We had an apprentice and we didn’t realise that when reaching a certain age the pay they receive is altered.
“As soon as we were made aware of this all back monies were paid straight away, please be aware it was only a month from the change of age.
“It made us feel physically sick.”
Employers are said to have taken deductions from wages for uniforms, underpaid apprentices and failed to pay back travel costs.
Each company will now have to repay the underpaid staff their wages and could be forced to pay a fine of 200% of the owed wages.
One business, Lyons Holiday Park Ltd, in Denbighshire, failed to pay a total of £7,321 to 12 workers.
Ben Williams, from the holiday company, said: “There were a small number of isolated cases identified, however all of these issues have now been rectified. We are a family run organisation, and pride ourselves on ensuring the welfare of our valued team members.”
He has declined to comment on an email which showed the firm tried to persuade a newspaper not to name it in a story about firms that failed to pay minimum wages to staff.
The highest average wage owed by any of the 14 companies was £1,762.43, while some owed as little as £26.74 per worker.
The 14 businesses
- Lyons Holiday Park, Denbighshire: Underpaid 12 workers a combined £7,321.01
- Nick’s Car Wash, Conwy: Underpaid three workers a combined £3,601.20
- Accent on Education, Newport: Underpaid nine workers a combined £2,293.23
- Aingarth Rest Home, Conwy : Underpaid nine workers a combined £1,836.60
- S R Motors, Carmarthenshire: Underpaid one worker £1,762.43
- Mansion House Llansteffan Carmarthenshire: Underpaid two workers a combined £1,087.13
- Sew 4 Sure, Swansea: Underpaid two workers a combined £616.36
- Restaurant James Sommerin, Vale of Glamorgan: Underpaid one worker £487.57
- Riverside Cantonese Restaurant, Cardiff: Underpaid eight workers a combined £346.39
- Diamond Cleaning, Conwy LL22: Underpaid 11 workers a combined £294.17
- Max Polish Shop, Carmarthenshire: Underpaid three workers a combined £285.04
- G.Williams & Son Butchers, Gwynedd: Underpaid one worker £257.82
- The New Sandon Garage, Cardiff: Underpaid one worker £220.73
- Owens Road Services, Carmarthenshire: Underpaid one worker £112.50
Secretary of State for Wales Alun Cairns said: “Paying less than the minimum wage is illegal, immoral and completely unacceptable.
“If employers break this law they need to know that we will take tough action by naming, shaming and fining them, as well as helping workers recover the hundreds of thousands of pounds in pay owed to them.”
Business Minister Andrew Griffiths said: “Our priority is making sure workers know their rights and are getting the pay they worked hard for. Employers who don’t do the right thing face fines as well as being hit with the bill for back pay.”
Wales had the fourth-lowest number of businesses underpaying staff, with the east of England, north east of England and Northern Ireland recording smaller numbers of offending employers.