In a statement on Monday, the organisation did not, however, say anything about the nature of the attack.
But a security industry source told iTWire that while there was no definite indication yet as to the cause, Windows ransomware was by far the most likely suspect.
There is some logic to this claim, with the number of ransomware attacks on healthcare organisations in the US rising by 60% in 2020 over the number in 2019. There were 92 individual attacks that affected more than 600 separate clinics, hospitals, and organizations and more than 18 million patient records.
Monday's Eastern Health statement said: "Eastern Health continues to manage the impacts of a significant cyber incident experienced last week.
"While a number of our IT systems remain offline, our Business Continuity Plans have been enacted and we continue to make inroads into our planned recovery.
"Thank you to our staff, patients and visitors for their understanding at this time.
"All patient information continues to be handled with the necessary care, confidentiality and due diligence.
"Eastern Health continues to accept patients at our three Emergency Departments.
"Any delays experienced with our Contact Centre have been rectified and we encourage patients and the community to utilise this service if they have any queries.
"COVID vaccinations for our prioritised staff continue across our sites, with our second staff clinic, Maroondah Hospital, opening today and Angliss Hospital on-track to begin later in the week."