The baby, named Cecilia Thomas, received a bullet in the head when shots were fired from another car in the South Shore neighborhood, according to police. She died shortly afterwards in hospital.
A 41-year-old man sitting in another car received a bullet in the face, but the condition is not critical.
The baby is one of the youngest victims of gun-related violence in Chicago. She would turn six months four days after she died.
So far this year, 282 homicides have been recorded in Chicago, which after all is a decrease from 316 in the same period last year. A total of 797 people were killed in the city last year.