The classified files, which were obtained by the ABC and are now with Australian Federal Police, contained information across five separate governments including documents relating to national security and defence.
The ABC has said one file contained highly classified documents that revealed insights into the National Security Committee, which is charged with decisions related to intelligence and security.
When pressed by media in Adelaide, Defence Industry Minister Christopher Pyne refused to comment on what the revelations will mean for Australia's relationships with key allies.
The prime minister's office has also refused to comment, simply issuing a statement about the investigation.
"The Secretary of the Department of the Prime Minister and Cabinet has initiated an urgent investigation into the circumstances around the disposal of two Commonwealth government filing cabinets that allegedly contained classified material," the office said in a statement.
"Given that the investigation is underway it is not appropriate for the Department to comment further at this time."
The breach in security comes a few months after restricted technical information of the F-35 Joint Strike Fighter (JSF), naval vessels, P-8 Poseidon, C-130 and the Joint Direct Attack Munition was stolen in a cyber attack.
In this instance, the cyber thief was able to gain access to the network of a 50-person aerospace engineering firm that had been subcontracted by the Department of Defence.