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.