The officers first used a Taser on the man when they arrived in the 7900 block of South Shore Drive around 11:45 p.m. and saw him stabbing the other man, police said. The Taser had "no effect," police said, and the man pulled out a hammer and ran toward the officers.
The department would not say whether the wounded officer shot herself or was hit by another officer as they fired at the man. More than 30 bullet casings could be seen at the scene of the shooting, down the street from South Shore Food & Liquors.
The man suffered several gunshot wounds and was pronounced dead at the scene, according to the Cook County medical examiner's office. Police said he was not carrying any identification.
The wounded officer was driven by another officer to Advocate Trinity Hospital, where she was treated for a graze wound to the leg and released.
Chicago Police Supt. Garry McCarthy, who was briefly at the scene, declined to speak to reporters at the hospital.
The man who was stabbed was taken to Northwestern Memorial Hospital in serious condition, police said in a statement.