The explosion caused a large fire to break out in the building in the Tariq al-Jadida neighborhood, a security source said.
One person was critically wounded, while several others were treated for smoke inhalation, the Red Cross and a hospital source said.
The blast left nearly 200 dead and thousands more injured as well as damaging tens of thousands of buildings in the capital.
It remains unclear what caused the initial fire which led to last month’s explosion, and though more than 20 have been detained as part of a probe into the blast, so far no one has faced justice.
Meanwhile, a series of fires and lesser explosions have taken place in the port, capital, and elsewhere since last month’s explosion, causing widespread panic among Lebanon’s residents who fear a repeat of the devastating blast.