There is concern that family doctors' surgeries could be struck on Monday when they open.
Ms Sturgeon said she was not aware of any ransoms being paid over the cyber attack but said that will be part of the police investigation.
They said: "This is an global cyber crime, committed on an unprecedented scale".
She told the Good Morning Scotland programme: "We invest heavily in cyber resistance".
On Monday issues still remained and blood tests at the four hospitals are "unavailable until further notice".
"One thing that is very important to stress is that there is no evidence that there has been any patient data compromised, so patient confidentiality hasn't been affected, but of course there will have been an impact on patients with some appointments cancelled".
"The message to patients is clear: the NHS is open for business".
NHS organisations across the country are on alert for a possible recurrence of Friday's cyberattack as staff return to work. "It was clear warnings were given to hospital trusts but this is not something that focused on attacking the NHS here on the United Kingdom". Again, if you have an appointment you should still attend unless contacted and told not to.
"In particular, making sure that our data is properly backed up and making sure that we are using the software patches, the anti-virus patches, that are sent out regularly by manufacturers".
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Security Minister Ben Wallace said the government used to contract for computer services across the entire NHS but that in 2007 - when the Labour Party was in power - that was stopped and left to the local trusts that run hospitals.
Meanwhile, a spokesman for the Prime Minister down played suggestions that NHS computers were particularly at risk of the WannaCry attack because many use WindowsXP, an older operating system. This prevented access to records and caused chaos throughout the NHS.
"This guidance was also reissued on Friday following the emergence of this issue".
Seven hospital trusts are still experiencing serious problems, among them St Bartholomew's Hospital in London, York Teaching Hospital NHS Trust and the University Hospitals of North Midlands Trust.
Problems with cyber security in NHS organisations were said to have been highlighted a year ago by Dame Fiona Caldicott, the national data guardian, who warned issues were given insufficient priority and health bodies persisted in using obsolete computer systems.
Dame Fiona and the Care Quality Commission wrote to the Health Secretary to highlight a "lack of understanding of security issues", according to the newspaper, and that "the external cyber threat is becoming a bigger consideration".
"The Health Secretary has been working round the clock on co-ordinating the NHS response to this, which has been a hugely impressive response".
However Ms Rudd strongly denied warnings had been ignored. A spokesman for May said the annual information technology budget in the NHS was 4.2 billion pounds and that an extra 50 million pounds had been allocated for updating cyber security.