The shooting took place Wednesday night in the 3500 block of West School Street near Avondale Park.
Antonio Bucio, 22, an alleged gang member, was charged with two felony counts of aggravated battery with a firearm and unlawful use of a weapon, police said.
Bucio allegedly got out of a van near the park and opened fire at a group of individuals playing basketball. The 7-year-old and a 2-year-old were hit by the bullets.
Chicago Police Superintendent Garry McCarthy said what happened involved a brazen disregard for life.
"I feel that it's critical that we stand here together and express our outrage that we're not going to allow these things to continue in our community," he said at a press conference Friday night.
McCarthy said Bucio is a known gang member and as part of the city's Violence Reduction Strategy, the suspect's associates will be singled by law enforcement.
"This group has gone to the top of the pile and we are going to ensure that they understand there are repercussions for their actions," McCarthy said.
The superintendent said the approach is different and dismissed notions that it was posturing by a new top cop eager to be seen as aggressively pursuing criminals.
"If they're selling drugs, we are going to lock them up for selling drugs. If they carry a gun, we are going to lock them up for carrying a gun. If they're wanted for warrants, we are going to arrest them for warrants. It will be ongoing and relentless," McCarthy vowed.
He credited community cooperation with delivering police leads that tracked down Bucio.
People who were in Avondale when the shootings happened seemed grateful.
"This never should have happened. And they [children] should be able to feel safe at a park or out in front of the house or on the street anywhere without having to worry about being shot, and they are traumatized about this," said Barb Oronowski, parent.
Alderman Rey Colon of the 35th Ward said he is not worried that going after one gang will embolden others.
"They're all doing this foolishness out on the street and they're all putting our children at risk," said Colon.
As a matter of policy ABC7 does not name gangs, but the area of Avondale has reportedly seen a vicious turf war going on between at least two groups for months.