Multiple rescue teams with sniffer dogs were searching the area after the wall collapsed during the night, said Sunil Deshmukh, a police officer.
Three other deaths occurred elsewhere in Mumbai, and Deshmukh said more casualties were feared at the site of another wall collapse.
The monsoon season in India brings heavy rains from June to September that cause flooding and other damage. Building collapses are common as the rains weaken the foundations of poorly built structures.
Monday's rains flooded roads in Mumbai and waterlogged train tracks. Thousands of railway passengers were stranded at stations overnight.
India's Central Railway said in a tweet that "nature's fury" made operating trains a "safety hazard" in some areas in the city. Trains were running at partial service Tuesday. Millions of passengers commute daily on a network of famed railways in Mumbai.
The city has witnessed incessant rainfall over the past few days and rain waters have entered homes, hampering normal life. A public holiday was declared for Tuesday and the Maharashtra state government, where Mumbai is located, said only emergency services would be functional.
Maharashtra's chief minister Devendra Fadnavis tweeted that weather officials forecast heavy rain on Tuesday. "People are advised to stay indoors unless there is any emergency," he said.
Weather officials said Mumbai has received the highest rainfall in a decade over a two-day period since Sunday, flooding homes in low-lying areas. TV channels showed footage of submerged cars and water flowing through ground floors of some residential buildings.
A domestic flight skidded off the main runway at the Mumbai airport late Monday night, and flight operations were partially restored on Tuesday. At least 50 domestic and international flights were diverted.
On Saturday, a wall collapsed on a cluster of tin-roofed huts housing migrant workers and their families in Pune following heavy rains, killing at least 16 people.