That means recipients trying to use the cards will have a hard time at the cash register, the St. Paul (Minnesota) Pioneer Press reported.
Target spokeswoman Molly Snyder said the problem can be fixed at the customer service desk.
"The actual number of cards impacted was less than 0.1 percent of the total sold during the holiday period," Snyder told the newspaper in an email Tuesday. "We are aware that some Target gift cards were not fully activated and apologize for the inconvenience."
KMSP-TV, Minneapolis, said Monday 40,000 gift cards were problematic.
"The numbers that have been reported in the media are much higher than what we experienced," Snyder said.
Target's toll-free number for gift cards is 1-800-544-2943.
Target, headquartered in Minneapolis, is the second-largest discount retail chain in the United States. The chain recently announced information from millions of debit and credit cards used at its stores between the end of November and mid-December had been compromised.