Nikhar Sadhu allegedly took a plunge into the Arabian sea from the Worli-end of the link at around 11:50 AM, said senior Police Inspector Gajanan Desurkar.
Another official said that Sadhu, travelling in a taxi, allegedly asked the cabbie to pull over saying he wanted to click some pictures.
However, he got down and jumped off, he said.
The cabbie called up the police control room, following which a team of police personnel was rushed to the spot, he said.
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He is yet to regain consciousness, the official added.
Police are investigating the trigger behind Sadhu taking the extreme step.
Further investigation is on.