The hackers posted a trove of apparently confidential documents online and claimed much more was to come from systems at CNAIPIC. So far less than 100 megabytes of data have been published but the hackers claim to have over eight gigabytes.
Links to the material were first posted on Twitter by @anonesc, one of many accounts that make announcements about the activities of Anonymous, a hacking collective that claims to have no formal leadership or structure.
Another Anonymous-linked account, @ AnonymousIRC, tweeted its support, saying "#AntiSec strikes at Italy government".
"Silent no more," it added. "AntiSec" is Anonymous' campaign against governments and the security industry.
The CNAIPIC files purport to contain information on an array of firms involved in critical infrastructure, including oil and nuclear firms, as well as government bodies such as the Australian Ministry of Defence.
The release follows the arrest earlier this month of 15 alleged members of Anonymous by Italian authorities, part of a global crackdown on the collective.
A public statement attributed to Anonymous at the time said those arrested were "peacefully protesting" for people's rights.