The NYPD says the officers opened fire on 35-year-old Victor Hernandez, a guard at Rikers, after he ignored numerous orders to drop a gun.
The officers say they fired only after Hernandez aimed the gun in their direction.
The encounter happened at about 3:45 a.m. Saturday in the borough's Morrisania section.
The NYPD says the officers were not in uniform, but wore badges around their necks and identified themselves as police.
They initially approached Hernandez after seeing a gun in his hand on the street. Police recovered a 9mm handgun at the scene. The gun was not a department issued weapon.
Authorities say he was taken to Lincoln Hospital for a wound to his arm. He was listed in stable condition.
Hernandez was charged with reckless endangerment and menacing.
The Department of Corrections also suspended Hernandez without pay. He has been with the department since November 2006.