According to the Daily Telegraph, authorities found the students were working "significantly longer hours" than their visas allowed at the Tesco-operated warehouse.
The breaches were discovered after immigration officials visited on the Tesco.com building in Croydon, south London.
It is understood UK Border Agency officials arrested 20 of the students for alleged breaches of visa terms that restricted the amount of hours they could work.
The Telegraph reports the the students, who were predominantly of Bangladeshi and Indian origin, had been working up to three-and-a-half times longer than their visas allowed.
A Tesco spokesman said: "In cooperation with Tesco, the UK Border Agency visited our dot com store in Croydon in July. As a result of this visit, a small number of staff were found to have breached the terms of their working visas.
"We continue to cooperate fully with the UK Border Agency as they look into this issue. We take our responsibilities as an employer very seriously and do not condone illegal working of any kind.
"We have a comprehensive system for ensuring all the correct procedures are followed in this area which has been externally audited and generally works well. We have now taken additional steps to ensure an incident of this nature does not happen again."
Philip Harman, partner on the employment team and head of the specialist immigration team at Cobbetts, told HR magazine: "The massive fines that Tesco are facing over breaching working practices should remind all businesses, large and small, that it is essential for management and HR to monitor their workers' immigration conditions. There are various types of visa and it is important to keep records to show that employees have the right to work in the UK and have complied with any conditions imposed by their visa.
"In this case, Tesco had employees that were on student visas and therefore were only entitled to work 20 hours a week. The employees may have excelled at their job and been eager to work the hours, but immigration rules are strict and Tesco should have been monitoring the situation to ensure that the limit on working hours was not exceeded. Immigration rules can be very unforgiving and it can be hard for an employer to prove that they did everything they could to ensure their employees were working legally if they do not have proper records and systems in place ."
