"Somebody had to have had access to the readers," she said. "These are devices that are sitting at the cash register. It is not easy to tamper with them."

Tampering with card readers is a growing problem, Litan said. But in most cases, such tampering involves ATM machines and card readers at gas pumps. "This is the first time I've heard of something like this," she said.

A spokesperson with Stop & Shop could not be reached for comment.