Edwards was caught by a sheriff's deputy in downstate Danville Saturday night.
Captain Michael Hartshorn, chief investigator with the Vermilion County Sheriff's Department, said the deputy pulled a vehicle over for a traffic violation near Bowman and Williams streets around 6:30 p.m.
Edwards was a passenger in the vehicle. He jumped out as it came to a stop and took off, Hartshorn said. The deputy chased him and caught him a block away.
Hartshorn said at the scene, Edwards gave the deputy a false name. Once he was brought to the county jail, he gave investigators his real name.
There is no word on when he'll be brought back to Chicago.
Police said two other men were involved in Tyshawn's murder. Corey Morgan allegedly lured the child into the alley where Dwright Boone-Doty allegedly shot the boy several times at close range.
Investigators believe the murder was part of a gang retaliation against Tyshawn's father, Pierre Stokes.