The party said they used 15-year-old Windows XP software which Microsoft stopped supporting in April 2014.
Computer expert Graham Cluley said hackers could potentially access confidential information when the machines are connected to the internet.
NHS Wales said there was "a very clear programme" to replace Windows software and called Plaid's figures "outdated".
Plaid claimed the Welsh NHS had 19,282 computers that use Windows XP technology, which Microsoft has stopped supporting against malicious software.
The party's health spokesperson Elin Jones said the situation reflected "a wider lethargy in utilising modern technology".
Mr Cluley told BBC Radio Wales on Friday that there was a potential security problem.
"If computers [using Windows XP] are connected to the internet, hackers might find a way to install malware, or Trojan horses, potentially to steal records and confidential data," he said.
The health service said it was taking steps to upgrade outdated computers.
A statement from its National Infrastructure Management Board said: "NHS Wales takes IT security very seriously and operating systems are one of several layers of security utilised.
"There is a very clear programme to replace Windows XP and we have prioritised the replacement of any devices that could impact patient care, implementing modern technology.
"The number of devices running Windows XP is reducing daily and the figures in the article are already now significantly outdated due to the work conducted both locally and nationally.
"There is no record of any technology not being implemented or delayed due to the presence of Windows XP."
Almost 20,000 NHS computers in Wales are in danger of being hacked into, Plaid Cymru has claimed.