Heartland Payment Systems, a major payment processing company, disclosed a data breach on Monday that potentially exposed tens of millions of credit and debit cardholders to the risk of fraud in what could quickly become one of the country's biggest data compromises.

Robert H. B. Baldwin Jr., Heartland's president and chief financial officer, said that his company believed the card numbers, expiration dates, and in some cases cardholder names were exposed after attacks on its computer systems at the one point...