Two-to-three multi-storey houses in a slum collapsed in the Mankhurd area of Mumbai on Sunday, leaving five young children and one woman dead, civic authorities said.
Rains also triggered landslides on the expressway connecting Mumbai with Pune, forcing its closure and disrupting traffic between the two cities.
Television images showed broken slabs of construction rubble on the road, while rainwater fell from the roof of a tunnel.
Besides road transport, flights were disrupted and long-distance train services, including those running between Mumbai and Pune, were also cancelled.
Local media showed residents trudging through waterlogged lanes, as schools and colleges were shut on Monday.
India's Meteorological Department issued a red alert on Monday for lightning, thunderstorms and heavy rain in Mumbai, advising people to avoid sheltering under trees or weak structures and avoid unnecessary travel.
Heavy rains have also led trees to collapse on Mumbai roads, killing at least three people since late last month, local media say.
The city, the financial capital of India, received more than 100mm of rainfall, with some regions receiving as much as 161mm of rain.
India's weather office has predicted "a spell of very light to light" rain for Monday at many places in the national capital region.
