Four of the new cases are residents on the third floor of the Ariele Apartments in Maribyrnong, which has been in lockdown since Monday evening.
Among them is a man in his 60s who subsequently infected his parents, who are aged in their 80s and live in Craigieburn.
The man attended an AFL match between Carlton and Geelong on Saturday and was seated in level two of the MCC section of the Melbourne Cricket Ground.
He also visited Highpoint shopping centre.
Some 200 residents of the Ariele Apartments were forced into 14 days of quarantine after a group of removalists from NSW conducted a pick up at the complex on Thursday while infectious.
The trio of removalists, two of whom have tested positive, did a drop off at a Craigieburn home the same day, as well as visited several petrol stations and fast-food restaurants, which have been listed as tier-one exposure sites.
The remaining new case is a man in his 30s who attended Coles Craigieburn on Saturday at the same time as a member of a family who recently returned from Sydney while infected with COVID-19.
Authorities said three members of the family flew into Melbourne on July 4, while a fourth drove back on Thursday.
The family, who live in the local government area of Hume, tested negative shortly after arrival but two became symptomatic and were swabbed again on Sunday, returning positive results on Monday morning.
A third family member tested positive on Tuesday, while the fourth tested positive on Wednesday.
The seven new cases will be included in Thursday's daily figures.
It comes as a war of words has broke out between the state and federal governments over financial support for NSW.
Prime Minister Scott Morrison on Tuesday announced a new federal support package following the COVID-19 outbreak in Sydney that has infected almost 700 people and claimed the lives of two.
The package will be jointly funded by the Commonwealth and NSW and offered to other states and territories if they have to impose extended lockdowns.
It was not received warmly by the Victorian government, which only received federal support during its fourth lockdown after repeated requests.
"Victorians are rightly sick and tired of having to beg for every scrap of support from the federal government," a spokesperson for the premier's office said in a statement on Tuesday.
"It shouldn't take a crisis in Sydney for the Prime Minister to take action but we are seeing the same double standard time and time again. His job is not to be the Prime Minister for NSW."
Treasurer Josh Frydenberg told ABC's 7.30 program people were "sick" of Premier Daniel Andrews' "whinging and his politicking of the crisis".
"Victoria was offered a 50-50 split and decided to reject it. Now we've put in place a system with NSW that can be extended and expanded to other states should they incur a lengthy lockdown," he said.
Industry Support and Recovery Minister Martin Pakula told reporters the federal government's treatment of Victoria and NSW has been "unequal".
"We've spent a year hearing about gold standard and now it's gone from gold standard to gold-plated support," he said.
"What we've seen in regards to NSW is support and comfort ... that's what should've happened here as well, rather than the extreme politicisation, the finger-pointing and the blaming that was going on from the federal government."
HOW THE NSW CORONAVIRUS OUTBREAK IS SPREADING THROUGH VICTORIA:
REMOVALIST CLUSTER
Cases:
* Two of a group of three NSW removalists have tested positive for coronavirus after they did jobs in Craigieburn and the Ariele Apartments in Maribyrnong on Thursday, July 8, while infectious
* Four residents from the third floor of the Ariele Apartments have tested positive
* A resident in his 60s has passed on the virus to his parents, aged 89 and 90, who live in Craigieburn
Exposure sites:
* Ariele Apartments, which is now in lockdown
* Highpoint shopping centre including The Reject Shop, SkinKandy and level 1 north car park, visited by the man in his 60s on Friday, July 9, between 11.10am and 12.35pm
* Level 2 of MCC Members' Reserve of the Melbourne Cricket Ground, visited by the man in his 60s on Saturday, July 10, between 4pm and 8pm
* ALDI Maribyrnong, near the apartment complex, visited by a case on Friday, July 9, between 5.30pm and 6.10pm
* Caltex and Hungry Jacks Kalkallo, visited by the removalists on July 8
* Mobil and McDonald's Ballan, visited by the removalists on July 8
HUME FAMILY CLUSTER
Cases:
* A family of four returned from NSW, three by car and one by plane on July 4 and July 8. All four have progressively tested positive since Sunday
* A man in his 30s who attended Coles Craigieburn at the same time as one of the family members
Exposure sites:
* Coles Craigieburn Central visited by one of the family members on July 10
* Metro Petroleum Broadmeadows visited by one of the family members on July 11