The chain advised its shops not to open on Saturday across the country, according to Swedish broadcaster SVT.
The supermarket does not believe that it itself was the target of the attack.
It is possible that the incidents could be related to a larger, international ransomware attack, the Swedish news agency TT wrote.
Ransomware attacks encrypt data on computers. The attackers usually demand a ransom for the release of the data.
Starting on Friday evening, there had been an attack on a service provider for Coop, which affected both the normal checkout systems and self-service checkouts of the supermarkets, SVT reported.
They had been working on the problems all night, but had not yet been able to solve them, a spokeswoman told the broadcaster.