Police were called to the 600 block of South Heald Street around 8:46 a.m. Wednesday following a 911 call about a suicidal man.
The 35-year-old was actively stabbing himself, police say.
When officers arrived they told the man to drop the knife.
Officials say the man refused, and then advanced toward a police officer. That officer then shot the man.
The man is hospitalized in critical condition for both the gunshot wound and what police say is a life-threatening, self-inflicted stab wound.
The police officer was not injured.
The Wilmington Police Department says this incident remains under investigation.