Police said Khairul Islam Khayer, ex-president of the unit, was attacked at Doctor Lane in West Rampura around 7:45pm on Friday.
They said the attackers were known to Khayer, 28.
His friends rushed him to Dhaka Medical College and Hospital (DMCH) around 8:30pm.
DMCH police outpost Inspector Mozammel Haque said two bullets hit Khayer in his left leg and left arm.
Khayer, however, did not reveal the identities of his attackers to police.