Home Retail Group has been fined £1.5m for not paying 37,000 Argos workers the national minimum wage.
The business said it was paying back current and previous workers £64 each, with the total cost coming to £2.4m.
If the company pays back HM Revenue and Customs within 14 days, it will only have to pay £800,000.
Sainsbury's said HMRC did the audit of Argos before the merger between the two companies and said it was seeking to deal with the problem as quickly as possible.
The fine handed to the group is bigger than that faced by Sports Direct when it was fined for not paying its workers the national minimum wage.
John Rogers, chief executive of Argos, said in a note to employees: "I am obviously disappointed to have to be giving you the news of this issue today, but Sainsbury's prides itself on open communications with colleagues and this includes when things don't go as we would like as well as when we are able to celebrate success."
The problem stemmed from workers coming in for a pre-work briefing, clocking on afterwards, and then queuing up for security checks when leaving the building. As they were not paid during the briefing, or during the time they were waiting to leave work, this meant their wage fell below the government's statutory minimum.
Sports Direct had also failed to pay the national minimum wage because it was not paying workers while they were queuing for security searches at the end of their shift.