In a statement on Friday, the organisation, which includes the Box Hill and Maroondah Hospitals, said it would contact patients as required as many of its systems were still offline.
"Eastern Health is still experiencing significant impacts related to the cyber incident," the statement said. The attack was said to have come to light last Tuesday.
"Thank you to our staff for their handwork continuing to deliver patient-centred care with many of our systems remaining off-line.
A report from security provider Tenable highlighted the fact that attacks on healthcare organisations had increased, with Windows ransomware by far the most common cause.
It said there 293 disclosed attacks in the 14 months to the end of February 2021, which led to the leaking of about 106 million records.
"While the events of 2020 have shone a bright light on the importance of the healthcare industry, it's also revealed to cyber attackers that there's a lot to be gained by targeting the sector," said Tenable research engineer Rody Quinlan.
"Personally identifiable information is valued at around US$150 per record, making the industry a lucrative target."