Angelique Styles, 60, was shot around 6:40 p.m. in the home she shared with her brother in the 10900 block of South Eberhart Avenue, according to authorities.
The woman then started approaching an officer with the knife and police shot her, Camden said.
In WGN-TV video from the scene, a woman identified by the station as a relative runs toward an area cordoned off with crime tape as police rush up. Someone restrains her as she screams, "Let me go! Let me go!"
Soon afterward, another woman and a man run toward the crime tape as someone shouts, "Jesus, God, Jesus!" and someone else screams, "No! No!"
The shooting was just blocks from where officers shot a man who stabbed a police sergeant Tuesday night. The sergeant received more than 50 stitches to his face, Camden said.
The Independent Police Review Authority was investigating the shooting, a spokesman said.