Target promises to honor the gift cards and said that only a limited number of the cards sold during the busy holiday season were affected.
Customers are advised to go to the guest services desk to sort out any gift card issues.
After the breach, Target had said that encrypted data was stolen but stopped short of identifying it as PIN numbers. The company issued a statement Friday saying that additional forensic work has shown that encrypted PIN data was removed along with customers' names and card numbers.
A PIN number is the personal identification code used to make secure transactions on a credit or debit card.
Data connected to about 40 million credit and debit cards used at Target were stolen between Nov. 27 and Dec. 15. Security experts say it's the second-largest theft of card accounts in U.S. history, surpassed only by a scam that began in 2005 involving retailer TJX Cos. In addition to the encrypted PIN numbers, the stolen data from Target included customer names, credit and debit card numbers, card expiration dates and the embedded code on the magnetic strip on back of the card.
Still, Target said it believes the PIN numbers are still safe because the information was strongly encrypted. The retailer said that PIN information is encrypted within its systems and can only be decrypted when it is received by its external, independent payment processor
"We remain confident that PIN numbers are safe and secure," said spokeswoman Molly Snyder in an emailed statement. "The PIN information was fully encrypted at the keypad, remained encrypted within our system, and remained encrypted when it was removed from our systems."
Minneapolis-based Target said it is still in the early stages of investigating the breach. It has been working with the Secret Service and the Department of Justice.
The Associated Press contributed to this report.