Harrowing CCTV footage shows the 25ft high coconut tree come crashing down and fall on unsuspecting Kanchan near her home.
The TV host, who works for the Indian government-run Doordarshan channel, is pinned to the floor in the footage by the weight of the tree.
She suffered fatal internal injuries and fractures as a result of being hit by it.
Onlookers rushed to help Nath by lifting the tree off her and carrying her several feet away, before she was rushed to hospital.
She tragically died on Saturday from brain injuries.
Resident Arjun Singh, who ran over after hearing the noise, said: "There was a lot of shouting and calling for help and a went over and saw the woman on the ground.
"I didn't know at the time it was Kanchan until after somebody said later. It's a shock that could happen, it could have been anybody who was in the wrong place at that time."
Kanchan, who was also a yoga teacher, was rushed to the Intensive Care Unit and Sushrut Hospital. She later died from the injuries.
TV colleague Rekha Rao said: "My dear friend Kanchan Nath renowned anchor of our music world has died. I will always miss you."
Kanchan's devastated husband Rajat Nath blamed the Brihanmumbai Municipal Corporation (BMC), the civic body that governs Mumbai, for the accident.
He said the BMC officials had been informed that the tree could fall anytime. But they had allegedly refused permission for the society to cut it.
Rajat said: "This incident happened because the BMC did not allow the society to cut the tree, despite being informed that it could fall any time."
Residents - including the couple - had signed a petition for the tree to be felled just months ago, according to reports.
Local ward representative corporator Asha Marathe said BMC officials had found the tree in good condition and had refused permission to cut it.
Asha said: "A team from BMC refused permission to cut the tree, as they had found it in good condition."
Meanwhile, colleagues at the Rangmanch Ke Sitare music awards which Kanchan had been due to host later this month, paid tribute to her and postponed the event.
A statement said: "A coconut tree felt down on Kanchan giving her major internal injuries like multiple fractures and some brain injuries too.
"We Team RKS and all the other members are really shocked and shattered at this point of time hence we have decided to postpone our celebration date."
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