A Melbourne council has become one of the first in the country to extend a ban on smoking in public places.

Boroondara Council, which covers suburbs including Camberwell and Kew, in the city's inner east, passed the motion in a vote last night.

The ban covers playgrounds, bus and tram stops, sports grounds and all council buildings within council boundaries.

Mayor Heinz Kreutz says the law was passed unanimously, but residents have nothing to fear.

"It's very much about education. We're not really interested in the fines as such," he said.

"So when someone forgets about this or has a cigarette near a playground, our local laws officers [will] have a conversation with them, explain what this is about and in nine out of ten cases we've found that people simply adopt the rule."

However, Mr Kreutz says repeat offenders will be fined.

He says for example if there is someone deliberately smoking near a three-year-old on a slide, who will not listen to reason, then they will be fined.

"With any law there needs to be some response, so we have a penalty point system and it may be anywhere between one and five penalty points, is between $1 and $500, depending on the severity of the disregard," he said.