In a statement, Science and Technology Minister Madeleine Ogilvie said the security of government information and the safety of Tasmanians remained of paramount importance.
The attack was announced on Friday by the government, more than a week after it was first made aware of the incident.
“We have referred the potential breach to relevant state and federal authorities, including police and the Australian Cyber Security Centre,” Ogilvie said.
More than 130 organisations worldwide have been attacked using a vulnerability in GoAnywhere, with the Cl0p ransomware gang claiming responsibility.
Cl0p has not made mention of any data taken from the Tasmanian government. Its website on the dark web only says that information about stolen data will be "coming soon".
An exploit for the bug in GoAnywhere being exploited was released on 7 February, according to the security firm CloudSEK.
“We are taking swift action to investigate this breach and ascertain if any information has been compromised. We will continue to provide updated information as it becomes available,” Ogilvie said.
“Our government reiterates that if the investigation reveals any personal information has been compromised we will work with anyone affected and ensure support is available.”
Contacted for comment, security firm Emsisoft's senior threat researcher Brett Callow said: "Cl0p claims to have compromised more than 130 organisations, and that means they’re potentially in possession of an enormous volume of information.
"As well as being used to extort the organisations from which it was stolen, the information can also be used as phishing bait to catch more organisations - and that’s something Cl0p has proven to be quite competent at."
He explained the second point by saying if Cl0p had stolen his emails and saw that he and I had been speaking about a mutual acquaintance Rick last month, the attackers could use that knowledge to convince me that they were him and get me to open an attachment or click a link.
What would be used would be something like, "Hey Sam – remember that conversation we had about Rick last month? Take a look at this update."