The deceased has been identified as Sudha Sridharan, a BMC official said.
The building had already been condemned as unsafe when it crashed down into a huge pile of concrete slabs, rubble and dust, Disaster Response Force commander Alok Awasthi said.
The building, located in Yashwant Nagar near Grand Hyatt Hotel, came down around noon on a chawl, an official in the BMC disaster management cell said.
Seven fire engines, two ambulances and a team of NDRF have been rushed to the spot.
While the building was officially uninhabited, some families were living there illegally, Awasthi said. Another dozen or so people had set up makeshift homes at the base of the building in the Santacruz suburb of India's west-coast financial capital.
"Our rough estimate is that there are around eight to 10 people feared trapped inside. Rescue operations are going on," he said.
Building collapses are common in India, where high demand for housing and lax regulations has encouraged some builders to cut corners, use substandard materials or add unauthorized extra floors.
(With PTI and AP inputs)