“Yesterday, we were the victims of a computer hack. We resumed operations in some stores overnight,” 7-Eleven said.
“We expect to open more during the day,” it added in its statement Tuesday.
The sudden outage occurred on Monday, a first for the US convenience store chain in Denmark, where it operates 175 stores.
It did not say who might have been behind the attack.
Five stores were so far open again, which were for now only receiving payments in cash or via a mobile phone application.
Based in Irving, Texas, 7-Eleven has than 77,000 stores worldwide which it operates either directly or under licence.