CCTV footage circulated online captures the precise moment the mezzanine walkway gives way, sending at least a dozen people crashing into the lobby area below.
Jakarta police spokesman Argo Yuwono said 77 people were being treated at four local hospitals, most with minor injuries. No fatalities were reported.
The 32-story twin tower complex, located on the busy Jalan Sudirman road of the Indonesian capital, is among the city's best known landmarks and houses the regional headquarters of numerous international organizations including the World Bank.
It was previously targeted by Islamist militants in a car bomb attack in 2000. But in a statement provided to reporters, a police spokesman ruled out the possibility of terrorism as a cause of Monday's collapse.
"This is purely an accident. This is what foreigners call a freak accident. It happened unexpectedly," said Police Inspector General Setyo Wasisto.
Valentina Simon, head of Institutional Relations at the exchange, told CNN the collapse happened at around 12:30 p.m. local time. She described the lobby as an open space where people would gather, and buy drinks and snacks from a coffee shop on the ground floor.
Many of those injured were accountancy students from the island of Sumatra who had been visiting the exchange, according to reports by CNN Indonesia.
A spokesman from Siloam hospital, where many of the students were being treated, said several of those injured were suffering from head and neck injuries, and doctors suspected some had bone fractures.
A CNN Indonesia correspondent said after the collapse the stock exchange director was shouting at people through a loudspeaker to evacuate the building.
Images on CNN Indonesia showed police cordoning off the area, and directing traffic and crowds from the site.
Officials have yet to identify the cause of the collapse. Indonesia has been known to have relatively poor construction standards, and corruption sometimes means safety checks are not always thoroughly carried out.
In a tweet, the Indonesian Exchange said trading would continue as normal "without significant change to the trading schedule."
The head of communication for the stock exchange, Oskar Herliansyah, confirmed to CNN that trading would resume as usual Tuesday.
Trading continued later Monday, with the composite index closed at 6,382.19, or 0.10 up.
Yosef Riadi reported from Jakarta, Angela Dewan reported from London. CNN's Yazhou Sun contributed reporting.