The eye of the storm narrowly missed the city, while nearby coastal areas to the south bore the brunt. The extent of the damage is still being assessed.
Officials moved tens of thousands of people along the coast to higher ground as the storm approached.
India's most populous city has 20 million residents and has also been badly hit by the coronavirus pandemic.
Mobile phone footage of the storm in Raigad, about 50km (30 miles) south of Mumbai, showed huge waves crashing into the shore, with trees being whipped into a frenzy by the strong winds.
There were warnings Nisarga may trigger big storm surges. Images showed it ripped tin roofs off buildings.
The man who died in Raigad district was hit by a toppling power transformer and died before doctors could get to him, the Press Trust of India reported. Eight others were injured.
However, in Mumbai, things were a little calmer.
"Winds have been stronger than what we've seen before, but the rain is a lot less than a bad monsoon day," reported the BBC's Yogita Limaye in the city.