Computers in thousands of locations have apparently been locked by a program that demands $300 (£230) in Bitcoin, the BBC reported.
There have been reports of infections in as many as 74 countries, including the UK, US, China, Russia, Spain, Italy, and Taiwan.
Many security researchers are linking the incidents together.
The UK's National Health Service (NHS) was also hit by a ransomware outbreak on the same day and screenshots of the WannaCry program were shared by NHS staff.
Read alsoReuters: Suspected Russia-backed hackers target Baltic energy networksOne cyber-security researcher tweeted that he had detected many thousands of cases of the ransomware – known as WannaCry and variants of that name –around the world.
"This is huge," said Jakub Kroustek at Avast.
Another, at cyber-security firm Kaspersky, said that the ransomware had been spotted cropping up in 74 countries and that the number was still growing.
Several experts monitoring the situation have linked the infections to vulnerabilities released by a group known as The Shadow Brokers, which recently claimed to have dumped hacking tools stolen from the US National Security Agency (NSA).
A patch for the vulnerability was released by Microsoft in March, but many systems may not have had the update installed.
Some security researchers have pointed out that the infections seem to be deployed via a worm – a program that spreads by itself between computers.
A number of Spanish firms were among the apparent victims elsewhere in Europe.
Telecoms giant Telefonica said in a statement that it was aware of a "cybersecurity incident" but that clients and services had not been affected.
Power firm Iberdrola and utility provider Gas Natural were also reported to have suffered from the outbreak.
There were reports that staff at the firms were told to turn off their computers.
Screenshots of WannaCry with text in Spanish were also shared online.
In Italy, one user shared images appearing to show a university computer lab with machines locked by the same program.
Bitcoin wallets seemingly associated with the ransomware were reported to have already started filling up with cash.
Another firm that confirmed it had been caught out was delivery company FedEx, though it did not clarify in which territories it had been hit.
"Like many other companies, FedEx is experiencing interference with some of our Windows-based systems caused by malware," it said in a statement.
"We are implementing remediation steps as quickly as possible."
Portugal Telecom also confirmed it was struck: "But none of our services was affected," a spokeswoman told the Reuters news agency.
And a spokesman for Megafon, the second largest mobile phone network in Russia confirmed some of its computers had been infected also.
"This is a major cyber attack, impacting organisations across Europe at a scale I've never seen before," said security architect Kevin Beaumont.
According to security firm Check Point, the version of the ransomware that appeared today is a new variant.
"Even so, it's spreading fast," said Aatish Pattni, head of threat prevention for northern Europe.