The baby, Jonylah Watkins, was struck by at least one bullet, authorities said, and died after surgery in Comer Children's Hospital in Chicago. Her father, Jonathan Watkins, 29, was hospitalized at Northwestern Memorial Hospital in serious-to-critical condition with a bullet wound to his left side and right buttock. A bullet also grazed his face, Police Superintendent Garry McCarthy said at a Tuesday news conference.
Police said the shooter approached on foot shortly before 1 p.m. and began firing while Watkins was standing by the minivan's open front passenger door and the infant lay on the front seat, the Chicago Tribune reported.
After shooting the father and baby, the gunman ran to a nearby parking lot and got in a blue conversion van, police said.
No arrests had been made but McCarthy said investigators were "pursuing several angles."
"We don't have one individual who's stepping up to help us," McCarthy said.
He said police had only a general description of the shooter, and it appeared Jonathan Watkins -- a gang member with an extensive record of drug possession and weapons arrests -- was "the intended victim, exclusively, the father."
McCarthy said police have parking lot surveillance video of what they believe is the getaway van, the Tribune reported.
Dominique Young, 21, the baby's aunt, said she and other relatives were walking on a nearby street when they heard about 10 "big gun shots."
Other family members said the girl's 20-year-old mother was working at a McDonald's at the time of the shooting. Relatives also told the Tribune she had been shot in 2012 while pregnant with Jonylah.