A man aged in his 60s returned a positive result this morning, and has been added to the four cases reported yesterday.
Acting Premier James Merlino said the man had symptoms prior to the first identified case, suggesting he could be the possible source case for the outbreak.
Chief health officer Brett Sutton said testing had determined the new cases were the "so-called Indian variant".
"It is as infectious as any other variant that has been reported historically, so it is by no means want to be complacent about," he said.
Meanwhile, New Zealanders who have visited Melbourne since 11 May are being advised to monitor themselves.
The cluster has prompted Victoria to reintroduce measures such as the mandatory wearing of masks indoors, and limits on both private and public gatherings from 6pm today (local time).
People will be restricted to five visitors per day to their homes, and public gatherings will be restricted to 30 people.
The restrictions will be in place until at least 4 June.
More than 14,800 test results were received yesterday, and 8269 vaccination shots were delivered.