Images on social media show pieces of ceiling and broken furniture in the lobby of the building in the Indonesian capital, amid clouds of dust.
The area has been evacuated and cordoned off by police, say witnesses.
A number of people were seen on stretchers being carried from the building.
An employee of the World Bank in Jakarta, based in the same building, told the BBC a mezzanine walkway above the lobby had come down.
He said he and members of his team were among those evacuated.
Police spokesman Argo Yuwono told local media that up to 15 people had been injured.
He said some of the victims, who had injuries to their hands and feet, had been taken to nearby hospitals.
Argo told Metro TV: "We are still investigating the cause, but for now our priorities are the casualties."
The incident happened shortly after 12 pm local time (05:00 GMT), according to a journalist from Metro TV who was in the building.
Marlia Zein added that there was a "loud banging", leading people inside to "immediately" run out of the building.
The stock exchange has re-opened for the afternoon session, with exchange chief Tito Sulistio saying the system was "not affected".