The bodies included in the lawsuit, which was filed in a US district court in Boston, are the Massachusetts Bankers Association, the Maine Association of Community Bankers, the Connecticut Bankers Association and a host of individual banks.
Bruce Spitzer, MBA spokesman said: "Our members say hot credit cards are still coming in, so we're not ready yet to assess the full extent of costs and thereby the damages. At a minimum it's going to be tens of millions of dollars."
News of the lawsuit follows TJX's announcement during February that information was stolen from an estimated 45.7 million debit and credit cards over a year and a half period.
Meanwhile a further 451,000 people who had returned goods without proof of purchase and were obliged to give their personal identity numbers and address also had their personal information stolen.
The MBA currently put the costs for the banks at as much as $25 million for each card.