"We're not able to tell you who's behind the attack. That work is still ongoing," she told BBC radio.
She said Britain's National Cyber Security Centre was working with the country's health service to ensure the attack was contained, while the National Crime Agency was working with them to find out where it came from.
Ms Rudd said the government did not know if the attack was directed by a foreign government.
On Friday, cyber extortionists tricked victims into opening malicious malware attachments to spam emails that appeared to contain invoices, job offers, security warnings and other legitimate files. Nearly 100 countries were impacted.
Ms Rudd said the attack was not specifically targeted at Britain's health service.
"(The virus) feels random in terms of where it's gone to and where it's been opened," she said.
Though 45 health service organisations in England and Scotland were affected by malicious software, no patient data has been accessed or transferred, said Ms Rudd.
The minister said lessons had to be learned from the attack.
"There will be lessons to learn ... Why is it certain regions are affected more than others? Is it to do with the software? Is it to do with better IT?"
Separately on Saturday, finance chiefs from the Group of Seven rich countries will commit to join forces to fight the growing threat of international cyber attacks, according to a draft statement of a meeting they are holding in Bari, Italy.
(Reporting by James Davey; Editing by Mark Potter)