The motive of the shooting is yet to be known.
The identity of another deceased was being ascertained, but is believed to be another security guard of the bank, police said.
The incident sparked off panic among customers who ran helter skelter at the Bhowanipore branch.
Both the persons were rushed to the state-run SSKM Hospital where they were declared dead.
The accused security guard was overpowered by other bank staff members who called the police which took him into custody.
The arrested was being interrogated to know the motive of the shooting.
The branch was closed down after the incident.