The mother and child are both being treated at Stroger Hospital.
The mother was in good condition Wednesday morning, and her baby boy has been stabilized after being shot in both legs.
Chicago police said this started just before midnight, when a man began shooting through the window of the garden apartment where they were.
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It took place in the 5200-block of West Congress Parkway, CPD said. Both were rushed to Stroger Hospital, as police continue to investigate whether they were the intended targets of the shooting or if it possibly could have been someone else inside the apartment at the time.
"We have to get these guns off the street, especially illegal guns, especially if that person is apprehended with that weapon," crisis responder Andrew Holmes said. "We need to find out where that weapon came from and how it got into the hands of individuals who don't need guns, and tougher penalties."
Nobody was in custody Wednesday, and no description of the male suspect or suspects has been released as of yet.
Area Four detectives are investigating.