Pride Asia of Bradford received a fine of £20,000 with £4,100 costs after being found guilty by Bradford magistrates of trading outside hours and failing to display opening hours correctly.
Store owner Abraham Quandah said: "We cannot pay a fine of this size. It is way out of proportion to the offence committed. If we cannot get it reduced we may have to close."
Abraham said he had been unaware of the detail of the Sunday trading regulations. He disputed evidence given to the court that inspectors from the council had written to the store to advise staff of the rules.
Under the law, stores with a floor area of more than 3,000sq ft can open only for one continuous six-hour period between 10am and 6pm on Sundays.
Inspectors told the court that they had been to the store at 7pm on a Sunday and found it open. They then returned later and measured the store, which was above the 3,000sq ft limit.
"We employ 26 people and they are all now in danger of losing their jobs," Abraham added.