Officers went to the area after getting reports of a man threatening to commit suicide.
Harrison said Adam Wade Carter, 25, was shot when he confronted the deputy with a knife.
Carter was taken to WakeMed, where he later died.
The deputy involved - Tavares Thompson - was not hurt. He has been with the Wake County Sheriff's Office for nearly five years. As a standard procedure, he has been placed on administrative duty.
Two witnesses were being questioned.
The State Bureau of Investigation was beginning a probe of the shooting - which is standard procedure.
This was the third shooting involving a law enforcement official in Wake County this week.
Monday night a Raleigh police officer was shot while responding to a suicidal man in the Brier Creek area. Officer A.W. Young was shot three times while trying to get into the apartment where Steven Meyer barricaded himself inside.
Officer Young survived and is recovering. Meyer was found dead from a self-inflicted gun shot wound.
Thursday night a Cary police officer shot at a suspect who allegedly tried to run him over. That incident took place near the Buffaloe Lanes Bowling Alley in Cary. The suspect, Randy Henderson Jr. was not hit and is now in jail on several charges.