The places include the iconic sea-facing Marine Drive promenade and the popular Girgaum Chowpatty beach, both major tourist attractions.
The decision was taken after a 18-year-old girl drowned in the sea while taking a selfie last week.
Last year, authorities imposed a “no selfie zone” at a Hindu festival due to fears they could cause stampedes.
Signs saying “no selfie zone” can be seen around the two festival sites in the state of Maharashtra.
Spokesperson for Mumbai police Dhananjay Kulkarni told the BBC that the places where taking selfies was risky included Bandra Bandstand, Sion Fort and Worli Fort, all places popular with tourists.
“The police will now approach the city’s municipality to prevent accidents at such spots due to people taking selfies. The municipality may deploy life guards and install warning signs,” Mr Kulkarni said.
The police warning follows Saturday’s incident when two girls trying to take a selfie near the sea in the Bandra area fell into the water.
One of them drowned, while the other was pulled out of the water by a local man.
In September a Japanese tourist died after allegedly slipping down the stairs while taking a selfie at the Taj Mahal monument in Agra.
Last year, the Russian government reportedly launched a campaign to make young people think twice before snapping selfies in risky situations.
In May, a 21-year-old woman survived accidentally shooting herself in the head while posing for a selfie with a gun in Moscow. There have also been several cases of children being electrocuted while taking selfies on top of railway carriages in Russia.
In August, a man in Spain was gored to death by a bull while taking a selfie at the annual bull running festival in the town of Villaseca de la Sagra.