Justice Secretary Michael Matheson said more than 120 public bodies were being contacted to ensure their defences were adequate.
He said NHS systems in Scotland were expected to be recovered by Monday and reassured patients with appointments they should attend as planned.
Eleven health boards as well as NHS National Services and the Scottish Ambulance Service were affected in an unprecedented cyber attack that hit scores of countries on Friday.
The attack impacted on acute hospital sites in Lanarkshire, as well as GP surgeries, dental practices and other primary care centres around the country.
Organisations across the globe, including investigators from the National Crime Agency (NCA), are working to hunt down those responsible for the Wanna Decryptor ransomware, also known as WannaCry.
Mr Matheson said the Scottish Government was liaising closely with the National Cyber Security Centre and NHS Scotland to identify the cause of the attack.
Ministers are to convene an extraordinary meeting of the National Cyber Resilience leaders’ board on Tuesday to review the response to the breach.
A “lessons learned” exercise will also take place to help mitigate the risks from further attacks.
The Justice Secretary said: “Friday’s attack has highlighted the need for everyone to have appropriate and robust measures in place to protect against cyber-attacks which could strike any IT system at any time.
“NHS Scotland systems are being recovered, we expect them to have returned to normal by Monday, and it is important to emphasise that there is no evidence that patient data has been compromised.
“Patients who have appointments booked for Monday and beyond should attend as planned.
“However, we must remain particularly vigilant against further incidents and the Scottish Government is taking action to enhance security, including contacting over 120 public bodies to ensure they have appropriate defences in place.
“One of the most common methods of infecting computer systems is through links and attachments in emails.
“Therefore I would urge everyone to think twice before clicking on attachments or links from sources that they don’t know.
“Police Scotland has been working closely with the National Crime Agency who are leading the UK-wide law enforcement investigative response, and this will continue.
“I would like to thank everyone at the NHS and other bodies who have been working round the clock to deal with this very serious incident and keep any impact on patient care to an absolute minimum.”
Speaking to ITV’s Peston on Sunday, Europol director Rob Wainwright warned that the threat from cyberattacks will only “continue to grow”.