The organisation, which runs the Box Hill and Maroondah Hospitals, said in a statement on Monday that there had been significant disruption to its services.
"Extensive work continues to be undertaken with the support of the State and Federal Governments, alongside industry IT experts," the statement said.
The attack occurred on 16 March and was made public a couple of days later.
Eastern Health has more than 50 facilities under its management and looks after the clinical needs of three-quarters of a million people.
"From a patient services perspective:
- "All three Emergency Departments remain open;
- "Category 1 Elective Surgery continues to be provided;
- "Additional Elective Surgery resumed today [29 March]; and
- "approximately 2/3 of all scheduled Outpatient clinic appointments continue to be provided.
"Further expansion of services will be safely reintroduced as additional systems are restored."
The organisation has yet to provide any indication of the cause of the attack, though there has been informed speculation that it is a ransomware attack.