Officers responded about 3:20pm on Monday to calls about a vehicle fatally hitting three people outside, ramming through the building and then hitting another person before exiting the other side, Chatham Police Department Deputy Chief Scott Tarter said.
Chatham is a small town of about 15,000 people just outside Springfield, Illinois.
Those killed were between the ages of four and 18, Illinois State Police said in a statement.
Several other people were hurt and taken to hospitals, police said.
The driver, who was uninjured, was the sole occupant of the vehicle, and was taken to a hospital for evaluation, Tarter said. Illinois State Police haven't said if the driver was arrested or taken into custody.
The building and facilities house YNOT Outdoors, which holds after-school programs and summer camps, according to its website.
"I am horrified and deeply saddened by the deaths of children and numerous injuries in Chatham this afternoon," Illinois Governor JB Pritzker said in a statement.
"My heart is heavy for these families and the unimaginable grief they're experiencing - something that no parent should ever have to endure."
He said his office was monitoring the situation and was ready to lend support.
It wasn't immediately known what led up to the crash or whether it was intentional.
The deaths in Illinois happened two days after 11 people were killed in the Canadian city of Vancouver when a car ploughed through a crowded street during a festival.
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