The department said the shooting unfolded in the 8300 block of Willow Place Drive when authorities were serving a warrant for aggravated robbery.
Investigators said they ordered two suspects to come out of the building when one male suspect attempted to climb out of a window.
A state trooper saw the suspect brandishing a gun, prompting law enforcement to open fire, striking the man.
The suspect was taken to the hospital and the trooper was not injured.
DPS Sgt. Richard Standifer told Eyewitness News that the two suspects were responsible for four robberies around the area.