The Cook County medical examiner identified the man killed as 19-year-old Quintonio Legreir and the woman as 55-year-old Bettie Jones.
Both victims were black and from Chicago.
Police did not disclose the race of the officer or release the officer's current work status.
The shooting comes at a time that the Chicago Police Department is the subject of a federal civil rights investigation, which came after the release of a video showing a white officer shooting a black teenager 16 times in 2014.
Jones was pronounced dead at 4:51 AM at Loretto Hospital.
Legreir was pronounced dead at 5:14 AM at Stroger Hospital.
Autopsies have not been scheduled, medical examiner's office spokeswoman Becky Schlikerman said.
The Chicago Police Department said in a statement that the shootings happened around 4:25 AM today after officers who responded to the call "were confronted by a combative subject."
Police said the shooting is under investigation and the case has been referred to the city's main police oversight agency.
Independent Police Review Authority spokesman Larry Merritt confirmed today that the agency was investigating an officer-involved shooting but had no further information.
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