Around 200 000 companies, hospitals, government agencies and other organizations in at least 150 countries have been affected by the malicious ransomware, which locked users' files and demanded payment to allow access.
Europol, the European Union's police agency, said it was concerned that the number affected would continue to rise when people returned to work on Monday morning.
However, few "ransomware" attacks have been reported so far.
In Sweden, the extortion attack, believed to be the biggest of its kind ever recorded, affected computers at engineering group Sandvik, Timrå municipal council and a small company in Västervik, according to Swedish Radio News.
There have been no fresh reports of attacks in Sweden, but the Civil Contingencies Agency (MSB), says it's too soon to say that the threat has disappeared.
Sweden has not been badly affected yet but it is hard to say if this will continue, it might get worse," Robert Jonsson, deputy head of cyber security at MSB tells Radio Sweden.
Security officials in Sweden have urged organizations and individuals to protect themselves from ransomware by updating their security software fixes, running anti-virus software and backing up data elsewhere. They warned that the malware could spread through computers with unpatched versions of Microsoft Windows.
The worldwide attack was so unprecedented that Microsoft quickly changed its policy and announced that it will make security fixes available for free for older Windows systems, which are still used by millions of individuals and smaller businesses.