Other banks are also setting spending limits to curb fraud following the breach.
(Read more: Target breach spurs suits, investigations)
Target has said that hackers accessed data on up to 40 million payment cards over 19 days through Dec 15 in the second-largest retail breach in U.S. history. It is not known who is behind the attack or how they accessed Target's network.
Debit cards, unlike credit cards, typically require customers to enter personal identification numbers when they make purchases at store check-out counters. Initial reports of Target's security breach said data may have been taken through devices at its counters.
Over the weekend, Target offered customers a 10 percent discount in its U.S. stores, after CEO Gregg Steinhafel said on Friday that the company would provide free credit monitoring to at-risk customers.
—By CNBC.com with Reuters