Imran Ismail, governor of Sindh province which includes Karachi, condemned the attack, saying it was “aimed at tarnishing our relentless war on terror”.
He said he had ordered security agencies “to ensure that the perpetrators are caught alive and their handlers are accorded exemplary punishments. We shall protect Sindh at all costs.”
Police said the attackers drew up outside the exchange in a saloon car and opened fire with grenades and automatic rifles.
Karachi was for decades notorious for its violence as the city of more than 20 million battled terrorism, ethnic strife and organised crime.
A series of intensive security operations have dramatically improved the city in recent years, but the BLA has managed to conduct a handful of high-profile attacks.
Suicide attackers struck the city’s Chinese consulate in November 2018, killing guards and civilians queuing for travel documents. Attackers from the group’s same suicide brigade attacked a hotel in the new port of Gwadar, north west along the coast from Karachi, in May 2019.