In a statement Switzerland's information security service Melani said there were 183 potential victims in Switzerland as of Sunday night.
On Monday morning Melani's director told news agency ATS that the figure was now around 200.
But that's a relatively small number of the estimated 200,000 infected computers in 150 countries worldwide, causing chaos in major companies and services including the National Health Service in the UK, Spain's national telecom provider Telefonica and US delivery service FedEx.
The so-called ransomware encrypts files on victim's computers and demands money in order to decrypt them. It is spread by using a known vulnerability in the Windows operating system.
To date no major organizations in Switzerland have been affected, though Melani said there may be thousands of potentially vulnerable computers.
Telecommunications company Swisscom, Swiss federal railways (SBB) and major Swiss banks and pharma companies have been in contact with Melani and taken preventative measures, reported news agencies on Monday.
The easiest way to protect yourself from getting a victim of WannaCry is to install the latest windows patches and always keep your system up to date, advises Melani.