The scam works by locking victims out their computers before demanding a fine of €100 to get their computer unlocked.
The virus causes a pop-up with the garda logo to appear and accuses the computer user of accessing illegal websites.
Ronanstown and Lucan Garda Stations are receiving an increasing number of reports from computer repair shops about the scam.
Gardai are warning people not to pay any fines.
According to the garda press office, anyone deceived into paying the fine should report it to his local garda station.
A victim of the scam from Lucan said: "This page popped up when I was browsing the web.
"It said I could have been watching pornography, downloading illegal files or looking at banned websites.
"It also said the gardai would be in contact to discuss this further; to get the internet back working until they arrive, pay a fee of €100."
"Your computer becomes locked. I tried to get off the page, but the toolbar wasn't there any more.
"I turned my computer off, but the pop-up was still on my page when I turned it back on. I turned it off again, and then it was gone."
Dublin Laptop Repair manager Ben Brennan warned people to be cautious of third-party applications, particularly on social networking sites such as Facebook.
"It comes through different sources: Facebook, email attachments, certain websites with malware embedded in their code. Half the cases we dealt with were Facebook-related. A lot of it is from the third-party games on Facebook."
These type of viral scams -- known as 'ransonware' -- first appeared in Russia in 2005 and have spread throughout Europe.
This scam -- known as 'the Police Trojan' -- targets victims with the police logo of whatever country they are in, demanding they pay a fine to have their computer unlocked.
It has been reported in at least 18 European countries; in Italy, 4,000 victims have been reported.