The UK security researcher "MalwareTech", who helped to limit the ransomware attack, predicted "another one coming... quite likely on Monday", the BBC reported.
The virus, which took control of users' files, spread to 100 countries, including Spain, France and Russia.
In England, 48 National Health Service (NHS) trusts fell victim, as did 13 NHS bodies in Scotland.
Some hospitals were forced to cancel procedures and appointments, as ambulances were directed to neighbouring hospitals free from the computer virus.
After taking computers over, the virus displayed messages demanding a payment of $300 in virtual currency Bitcoin to unlock files and return them to the user.
MalwareTech, who wants to remain anonymous, was hailed as an "accidental hero" after registering a domain name to track the spread of the virus, which actually ended up halting it.
"We have stopped this one, but there will be another one coming and it will not be stoppable by us," the 22-year-old told the BBC on Sunday.
He also warned hackers could upgrade the virus to remove the "kill switch" that helped to stop it.
"Version 1 of WannaCrypt was stoppable but version 2.0 will likely remove the flaw. You're only safe if you patch as soon as possible," he tweeted.
Investigators are working to track down those responsible for the ransomware used on Friday, known as Wanna Decryptor or WannaCry.
The virus exploits a vulnerability in Microsoft Windows software, first identified by the US National Security Agency.
(Except for the headline, this story has not been edited by NDTV staff and is published from a syndicated feed.)