The signage collapsed at a petrol station in the city's east, trapping dozens of people underneath.
"So far, 60 people have been rescued from the accident site and admitted to hospital. Four people have died," a statement issued by municipal authorities said.
The collapsed billboard measured 70 by 50 metres, according to a post on social media platform X by Mumbai's police force.
Mumbai was hit by strong winds accompanied by rain and dust storms on Thursday that uprooted trees and caused brief power outages in parts of the city, along with disruptions to the city's train network.
Indian media reports said flights were temporarily suspended at the city's international airport with at least 15 planes diverted.
Devendra Fadnavis, the deputy chief minister of Maharashtra state, said the injured were being treated at Rajawadi Hospital.
A "high-level inquiry has been ordered into the incident," Fadnavis said in a post on X.
