Early Warning Network said in a statement on its website on Monday that the unauthorised alerts were sent on Saturday night.
It said the alerting system was accessed at about 9.30pm on 5 January, and a "nuisance message' sent out to some subscribers whose addresses were in its database. Email, text and landline messages were sent.
"EWN staff at the time were able to quickly identify the attack and shut off the system limiting the number of messages sent out," the company said.
The bogus messages said: "EWN has been hacked. Your personal data is not safe. Trying to fix the security issues."
The statement said the police and the Australian Cyber Security Centre had been notified.
EWN said no personal information had been exfiltrated as a result of the hack.