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Premier Daniel Andrews on Tuesday confirmed just 28 of the cases were linked to known outbreaks, while 242 remain under investigation.
Chief Health Officer Brett Sutton said the jump from Monday's 177 cases proved there was some way to go before the outbreak reaches its peak.
"It's not as high as our biggest single day, but we haven't turned the corner yet," Professor Sutton said.
"I hope to see that this week, but there are no guarantees."
The state now has a total of 4224 cases, of which 1803 remain active.
"That's a really significant number of people with coronavirus and it does mean that in the next fortnight, we're going to see a number of people who will require hospital," Prof Sutton said, noting about 10% to 20% of people with the virus require hospitalisation.
"A couple of hundred individuals at least will require hospitalisation in the next couple of weeks."
Currently 85 infected people are in hospital in Victoria, with 26 in intensive care, an increase of nine from Monday.
Twenty-one people are on ventilators.
Some residents of Menarock Aged Care in Essendon have been transferred to hospital after 28 staff and residents contracted the virus.
Prof Sutton said not all residents need to be transferred to hospital.
It is the largest aged-care cluster of coronavirus in Victoria.
Some 80 staff and residents across aged care facilities have tested positive to Covid-19, Prof Sutton said.
Meanwhile, further restrictions may be considered to curb the spread of community transmission.
"We would do the minimum required, because we know how much of an imposition it is on businesses and people's lives, but if it's required to reduce transmission, then it has to be in play," Prof Sutton said.
The premier said it was "too early" to decide on further restrictions, noting metropolitan Melbourne and Mitchell Shire was just one week into a six-week lockdown.
"It'll take as long as it takes, but it will be a shorter lockdown if everyone comes forward and gets tested when they're ill, follows the rules, only go out of your house for a lawful purpose and when you need to," Mr Andrews said.
The premier said paramedics and a number of staff from Jetstar, Medibank, Telstra and Qantas will joining the public health team to help with the massive task of contact tracing.
"It makes sense for us to call upon them as our task gets bigger and bigger," he said, adding a number of staff from banks also would receive training if required.
About 1000 Australian Defence Force personnel are also heading to Victoria to help enforce the state's lockdown and testing.