Karachi police chief Ghulam Nabi Memon said the attackers pulled up in a vehicle outside the trading floor and hurled a grenade at the building before opening fire.
The Pakistan Stock Exchange said in a statement that the situation was "still unfolding".
The BLA along with other militant outfits have always been fighting for secession of the southwestern Balochistan province, which they claim was forcibly incorporated into Pakistan when it was founded in 1947.
Gunfire was heard following the attack as the police moved in to cordon off the area.
"Clearance operation is under way in the stock exchange building and Pakistani authorities say their timely action has foiled a major terrorist attack there", journalist Kamran Yousaf told TRT World. The Pakistan Stock Exchange confirmed that no militants made it into the building.
It is not clear how many assailants are involved or who they are.
The stock exchange has offices for hundreds of financial institutions and is situated in a high security zone along with head offices of banks and other businesses.
PSX Managing Director Farrukh Khan said that the "number of people in the compound was lower than normal today as many people are still staying home due to the Covid-19".
MapWhy are Baloch groups fighting?
No militant group has claimed responsibility for the attack.
"The terrorists did not succeed in any of their targets and the attack, which holds similarities with the Chinese consulate incident, will be thoroughly investigated". All staff inside the building were unharmed.
Impoverished Pakistan has repeatedly turned to Beijing for investments and loans including under the $54-billion China-Pakistan Economic Corridor (CPEC) that Western critics say will be of greatest benefit to China in the long run. Widescale abuses and repression by the Pakistani military have been documented over decades in the province, which is hard to access by journalists and human rights groups.
In May 2019, the BLA warned China of dire consequences if Beijing did not quit CPEC projects in Balochistan.
The assailants from the BLA, which opposes China's Belt and Road projects, also had a hidden cache of food and supplies, hinting at a possible hostage scenario, according to police.