The medical examiner has identified the 19-month-old child as Eboni Richardson.
The shooting took place Thursday night near U.S. Steel Yard, where the Gary SouthShore RailCats were to play about an hour later. The game went on as scheduled.
The 20-year-old father was in critical condition on Thursday night at Methodist North Lake Hospital.
The shooting took place in the suspect's SUV.
The toddler's mother's relatives were either just arriving or had just arrived moments after the shooting.
"Some of his relatives pulled up in a car and at some point, I don't know when or what prompted it or whatever, but he fired one shot into his baby's chest area and the baby died from a single gunshot wound to the chest and then he turned the gun on himself," said Gabrielle King, Gary police spokesperson.
Police have released the name of the father, but ABC7 is holding it until he is charged.
The Associated Press contributed to this report.