The deceased was identified as Hanif Mia alias Shahin Biswas, 48, son of late Buddia Uddin of Rupganj in Narayanganj district.
Rab stopped an auto-rickshaw during its regular patrol in front of Kidney Diseases and Urology Hospital in the area around 11pm, said said Muhammad Mohiuddin Faruqi, superintendent of police, Rab-2.
Three men, including the driver, stepped out of the vehicle and abruptly opened fire while another person fired shots from inside the auto-rickshaw.
After the skirmish, Rab arrested Hanif and took him to Dhaka Medical College Hospital where the doctor pronounced him dead, Rab SP added.
A foreign pistol and six bullets were recovered from the spot while the auto-rickshaw was seized.
The other criminals managed to flee the spot.