Interior Minister Nohad Machnouk said Blom Bank was the target.
The Lebanese Red Cross said two people received minor injuries, the National News Agency reported.
Smoke rose from the Verdun area of Beirut after the blast. Local television showed footage of a damaged building and said shattered glass had fallen to the ground from several storeys up.
A security source said the bomb had contained 2 kg (4 lb) of explosives.
Machnouk said it had been left in a bag by the back wall of the building.
“Politically it is clear that target was Blom Bank only,” he said, adding that the attack had nothing to do with the militant group Islamic State, which has mounted suicide bombings in Beirut. Machnouk said initial reports indicated there had been no fatalities.
The last bomb attack to hit the Lebanese capital killed more than 40 people in the southern suburbs, an area where the Shi’ite Muslim Hezbollah group is dominant. That bombing was claimed by the Sunni Muslim Islamic State.
Blom Bank has closed a number of bank accounts belonging to people suspected of links to Hezbollah to comply with a U.S. act targeting the Shi’ite group’s finances, Lebanese officials have said.