The incident occurred near Leela Hotel in suburban Marol when a huge slab caved in this afternoon, disaster management department of the city's municipal corporation said.
While one person, believed to be a construction worker employed at the site, was declared dead on arrival at the Seven Hills Hospital, another man is admitted there in a critical condition with serious chest injuries.
Five others admitted to Seven Hills Hospital and as many at Cooper Hospital are stable, sources said.
Cranes and other heavy machinery have been deployed to clear the huge debris.
The island city and suburbs received heavy downpour yesterday and early this morning.
This part of the overhead Metro bridge is on the crowded Andheri-Kurla road that leads to the airport.
The collapsed bridge is part of the much-delayed 12-km Versova-Andheri-Ghatkopar corridor of the Mumbai Metro.
Meanwhile, reacting to the tragedy, Reliance Infra which is constructing the Metro railway said in a statement that its emergency response team was at the site for rescue operation.
The statement said, "we deeply regret the accident at the airport station metro site, which is being constructed by our contractor HCC.
"Our emergency response team along with HCC staff is at the site to provide rescue and relief services which is the immediate priority."
The company also clarified that the length of the bridge that collapsed is 15 meters and not 50 meters as was being reported.