The employee, who has since been sacked, is believed to have introduced the Metrion Cascade 111 virus to the system while playing a computer game.
The virus, which infects executable files and overwrites batch and HTML files, infected 200 PCs. Network managers switched off the entire system to halt its spread.
The council suffered a virus attack in February that cost £10,000 to fix.
Council IT chiefs said both incidents had been well handled.
The local branch of trade union Unison questioned the level of IT training for staff and their knowledge of the council's security policy for dealing with viruses.