J.P. Morgan Chase & Co. on Saturday put in place daily limits on use for debit-card holders who shopped at Target Corp. stores during a 20-day security breach, a move showing how banks may try to contain their exposure to the massive data theft.

In a letter to debit card holders posted on its website, Chase said such limitations on spending would be temporary while it reissues cards. For the affected cardholders, the bank is limiting daily cash withdrawals to $100 and putting on a $300 daily purchasing cap. The spending...