Councillor Richard Foster described his plan as a step in offering the city an alternative to the worsening congestion that clogs the inner city and suburbs.
"This is just about getting people used to the idea ... and over time, obviously well into the future, we may well see a time when we don't have cars in the city at all," Foster told ABC News this week.
He said that people should be urged to embrace other ways of getting about, as an alternative to driving private vehicles into and around the CBD.
"It's about saying on this particular day, between these particular times, we don't want cars in the city - we want you to use public transport, want you to get on a bike if you can and if you've got one, or walk into the city if you're close by," Foster said.
Commercial vehicles, taxis and emergency services vehicles would all be exempt, he added.
Melbourne Lord Mayor Robert Doyle, and Victorian Premier Daniel Andrews, have both dismissed the idea as an unworkable proposal.
"It's a complete thought bubble, it started as a good idea ... in a smaller street that's not in the centre of the city, [but] it is completely overreaching to suggest that we might keep cars out of the city altogether," Councillor Doyle said.
Premier Andrews echoed the mayor’s sentiments, describing the proposal as an idea that’s “not the real world”.
"Only people who live very close to the city and perhaps don't drive a car could up with an idea like that," he said during an interview on the Southern Cross Austereo radio network.
Councillor Foster highlighted the cities of Paris, Bristol and Buenos Aires as examples of areas that have run successful car-free trials.
"If they can do this right, there's no reason why we shouldn't start considering ideas like this too," he said.
Foster’s proposal follows comments from the head of VicRoads, John Merritt, who said in July that motorists should begin looking to public transport and cycling to avoid congestion.
“We need to invest heavily in public transport, which we are, through Melbourne Metro and we need to encourage people to cycle or to walk and make that feel as safe and as practical as we can,” Merritt said.