The Premier League club are among 179 employers on a list released by the Business Department, which also included Birmingham City FC and rugby clubs St Helens and London Irish.
Restaurant chain Wagamama was named as the worst offender, followed by TGI Friday’s and hotels giant Marriott.
The Government fined the employers a total of £1.3m after £1.1m in back pay was identified for 9,200 workers.
According to the Business Department, Stoke City failed to pay £1,102 to seven workers.
The club are owned by Denise Coates, the billionaire founder of betting firm Bet365, who paid herself more than £200 million in 2016.
A Stoke City spokesman said: “Once this matter was brought to our attention we moved swiftly to repay the money to the members of staff concerned.
“The issue arose from our now historical practice of allowing staff to pay for tickets and retail merchandise voluntarily purchased from the club via deduction from their monthly salaries, for which the employees gave written permission for deductions to be made.
“Employees are now no longer permitted to purchase match or club lottery tickets or items from the club shop via such a wage deduction scheme.
“As a result, the reported breach will not recur and the club is confident that we are now fully compliant with all current regulations.”
The Business Department figures showed Wagamama failed to pay £133,212 to 2,630 workers, TGI Friday’s shortchanged 2,302 of its staff to the tune of £59,348, and Marriott underpaid £71,723 to 279 employees.
Business minister Andrew Griffiths said: “There are no excuses for shortchanging workers.
“This is an absolute red line for this Government and employers who cross it will get caught – not only are they forced to pay back every penny but they are also fined up to 200% of wages owed.
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“Today’s naming round serves as a sharp reminder to employers to get their house in order ahead of minimum wage rate rises on April 1.”
On that date, the National Living Wage will go up from £7.50 to £7.83 per hour.