Yesterday night's attack was the latest violence in a city that has struggled to stop such shootings by increasing police patrols.
Three people were in critical condition. The others were reportedly in serious or fair condition.
Police said no arrests had been made.
The child's uncle, Julian Harris, told the Chicago Sun-Times that dreadlocked men in a car shot at him before turning toward nearby Cornell Square Park and opening fire. He said his nephew was shot in the cheek.
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Police officials declined to discuss details of the investigation.
Among the 13 victims were at least two minors, ages 15 and 17.
The Rev Corey Brooks spoke with the 3-year-old's family members and said the boy was resting with his mother.
"He was talking when they first brought him in, but he's heavily sedated now," he said.
"They say he's good," said Semecha Nunn, the boy's grandmother. "They going to have to do a little plastic surgery on him, but he's OK."
A 30-year resident, she said she was surprised by what had happened. She told the Sun-Times there hasn't been much gun violence in the neighbourhood in recent years.
The shooting comes nearly three weeks after Chicago saw an outburst of violence over the Labour Day weekend that ended with eight dead and 20 others injured.