The boy -- identified as Deon Williams -- was transported in serious condition to Comer Children's Hospital, but later pronounced dead, police said shortly before 5 p.m.
Preliminary reports from Chicago police indicate that the weapon accidentally discharged.
Police search for teen who accidentally shot 13-year-old boy
Williams' sisters said the gun was brought into the house by a friend of their brother and it was the friend who was in possession of the gun when it discharged.
"My niece was in the bedroom when it happened. My little brother was sitting at the mirror in my room and the little boy was playing with the gun that he brought from his house, and he was playing with the gun and made a mistake and shot the gun off," said sister Peaches Johnson.
The incident occurred at about 3 p.m. in the 7300 block of South Aberdeen Street on the city's South Side.
Williams, who was a seventh grader at Mays Elementary Academy, was shot in the chest.
Boy, 13, fatally shot in Englewood
No one was in custody Sunday night. Williams' father urged the teenager who apparently misfired the gun to turn himself in.
"I have no ill feelings for him. I just want him to turn himself in," said the victim's father, Donald Williams.
Donald Williams said organs and tissue from Deon will be donated to help other children.
Chicago police are investigating.
A candlelight vigil was scheduled for Sunday night.
Boy, 13, dies after being accidentally shot in the head