This happened Sunday evening near the intersection of Roosevelt Road and Independence Boulevard on the West Side.
Police were still on the scene late Sunday night as they continued to go over the evidence in the parking lot of a Church's Chicken.
The incident took place around 7 p.m. Sunday and elicited a massive police response, as usually occurs when a Chicago Police officer is injured.
The incident began when Illinois State Police, who were already in the parking lot investigating a man suspected of abducting a child from the suburbs, flagged CPD down for help.
Police said that in an attempt to get away, the offender allegedly ran over a Chicago Police officer, breaking his leg.
Police then shot the offender, critically injuring him.
"I heard a lot of gun shots when I came up," said witness Michael Johnson. "I looked over and I saw an officer on the ground. That's when the other officer, I guess he was searching around, he opened the back, there was a baby in there and he proceeded to do what he did and that was to get the baby out."
The injured officer is at Northwestern Memorial Hospital with a broken leg.
The Fire Department confirms that they did transport a young girl to Mt. Sinai with what is described as minor bumps and bruises.
There was a police vehicle at the scene from Bridgeview, which may be where the child is from, but Bridgeview Police are not commenting.