Vanilla Lounge, an Eaton Mall business, was listed on Wednesday as a Tier 1 exposure site to COVID-19, amidst the ongoing outbreak in Victoria.
A case visited the venue at the south-east Greek-dominated suburb on Friday 9 July between 2.45pm and 4.30 pm while infectious.
Anyone who attended the venue during that timeframe should immediately isolate, get tested and quarantine for 14 days from the date of exposure.
The business posted an update for customers on its temporary closure.
Victoria recorded two new COVID-19 cases on Thursday following a tally of 10 on Wednesday.
Meanwhile, unconfirmed reports state that Victorian officials are considering implementing a short snap lockdown of three to five days, with details still being decided.
Commenting on the two latest identified infections on Thursday afternoon, Victorian COVID-19 Commander Jeroen Weimar said they were both linked to the MCG, but there was no obvious relationship between them and they were sitting apart.
"This is possibly two examples of stranger-to-stranger transmission between the individuals that we know about," he said.
"We do not believe they are known contacts of the other two positive cases we know were there.
"That gives us significant cause for concern."
