The act bans Tasmanian retailers from supplying shoppers with lightweight plastic shopping bags. However, it does not include bags that are biodegradable, resealable zipper storage bags, heavier plastic bags (used by clothing and department stores) and plastic bags that are part of packaging for items like bread, frozen food or ice bags.
The Mercury reports the council accepted a motion to phase out plastic containers and Hobart alderman Bill Harvey said it would set an example for the whole country.
"This is something that I think will have an impact on society," he said.
"It's time to start moving on an issue like this and the council can be a national leader."
Deakin University's hazards material management lecturer Dr Trevor Thornton said it was a good move, but Hobart needed to be careful.
"For example, with plastic shopping bags, sometimes the alternatives are not that better environmentally," he said.
"What we need to do is determine why we're doing it, what are the outcomes, what we're looking for, and move from there. Is it the resources, litter, waste, cost, all of the above?
"The bottom line is we have to be cautious about swapping one issue for another issue.
"Plastics are not always an evil, they can be good depending what we are using them for."
Dr Thornton said it was possible to phase out the plastic containers in three years if retailers co-operated.
"When reusable coffee cups came in a lot of cafes said they wouldn't fill them up, people weren't washing them or whatever. But often looking at those alternatives, the hot water and detergent to clean them can outweigh the single disposable use. You have to do the sums and work out what is best," he said.
Dr Thornton believed it would be harder for people if plastic takeaway containers were banned altogether.
"I remember going to the takeaway shop and my parents would bring saucepans from home for the fried rice or whatever to be put into them," he said.
"It's not such a silly idea, but we're in a different world now and working late and picking up meals on the way home.
"Is it possible if I frequent the same takeaway or convenience store, can I have reusable packaging I rinse and take back? But then that's impacting on food safety and those sorts of issues."
Dr Thornton said the best option would be biodegradable takeaway containers that could be put into compost bins at night.