The City of Fremantle has become the first council in Australia to ban the use of non-degradable plastic bags in shops.

Councillors voted last night to outlaw single-use bags.

Retailers who continue to supply non-degradable bags will face an initial fine of $150, while repeat offenders could be fined $5,000.

Fremantle Mayor Brad Pettitt says the ban will be phased in over six months to give businesses and residents time to adjust.

"That will give retailers an opportunity to start that process - educate their customers, order in new bags that are compliant with the local law," he said.

Mr Pettitt says he hopes the idea will now be adopted by other councils across Western Australia.

"Most of the world has some kind of restrictions on single use plastic bags, so I think WA will catch up to that and we're really happy to be at the cutting edge of that," he said.

"We can start to iron out some of those challenges as we educate our community, and we hope then we can see the whole State taking this approach."

The law must now be tabled before Parliament for consideration, but the council is confident it will be accepted.

The communities of Coles Bay in Tasmania, Mogo in New South Wales and the Sydney suburb of Oyster Bay started phasing out single-use bags almost a decade ago.

The South Australian Government outlawed entirely them in 2009 while the Northern Territory and ACT followed suit in 2011.

The Tasmanian Government is also intending to do the same.