The computers, which controlled information screens in the city, are not linked to the municipality’s main I.T. system, reports newspaper Politiken.
The screens are placed on roads entering the central Jutland town and are usually used for advertising the local nature centre or candidates for pensioners’ committees, writes the newspaper.
But on Friday they showed a ransom-demanding screen that appeared on systems in scores of countries hit by the global cyber attack.
The software attacks use a technique known as ransomware that locks users' files unless they pay the attackers a designated sum in the virtual currency Bitcoin, reports AFP.
The ransomware demands payment of 275 euros in Bitcoin within three days or the price is doubled, and if none is received in seven days, the files will be deleted, according to a screen message.
Reports Saturday suggest that Denmark has escaped from the cyber attacks relatively lightly.
Britain's National Health Service declared a the attack a "major incident" after dozens of its hospitals were hit on Friday.
Also affected by the onslaught were Russia's interior ministry, French carmaker Renault, the Spanish telecom giant Telefonica and the US delivery firm FedEx, as well as German rail operator Deutsche Bahn and a municipality and technology company in Sweden.
“On the screens there was a picture demanding money, and our supplier told us that it was ransomware,” Randers Municipality’s head of communications Karen Balling Radmer told Politiken.
The affected computers in Randers are a physical component of the screens.
Radmer told Politiken that the municipality would not be paying any ransom.
“We will not be supporting criminals that do this kind of thing, because what would come next? Our suppliers are looking at the computers now and they will probably be wiped and started from scratch,” she said.
Randers Municipality has switched off all six of the affected screens, which are fortunately not connected to the main I.T. systems of the city administration.
Friday's wave of cyberattacks, which affected dozens of countries, apparently exploited a flaw exposed in documents leaked from the US National Security Agency.
Microsoft released a patch to protect against vulnerability to the ransomware in March, but many systems may not have been updated, reports AFP.