Target will honor affected cards, Snyder said.
"If a guest discovers that their gift card has not been activated, they can bring it to the guest service desk at their local Target store or call 1-800-544-2943 for assistance," she said.
The company did not respond to requests for comment on how it would determine the balance that should be loaded onto the card.
Most retailers' systems can track gift cards by looking into records for the card, including the point of sale, according to Horne.
"If they have the card number, they should be able to track it," he said.
The incident reinforces an important point for shoppers, whether they are buying a gift card, getting one for free with a purchase or receiving one for store credit after a return.
"Whenever you get a gift card, make sure you keep the receipt in case it didn't take," said Edgar Dworsky, founder of ConsumerWorld.org. "If you really want to be thorough, call the toll-free number on the back of the card and check its balance."
—By CNBC's Kelli B. Grant. Follow her on Twitter @Kelligrant and on Google.