One of the girls was an infant less than a year old, Debbie Delaney, whose husband is mayor of Emington, said. The other girl was in second grade and the boy was in kindergarten, the Chicago Tribune reported.
The two girls were found in the back yard with their mother, while the boy and the man were found elsewhere on the property, the newspaper said.
Delaney said police were not searching for any suspects but she did not know what led to the shooting.
"I have no idea," she said. "No clue, no clue."
Neighbors told the newspaper the family had kept to themselves for the most part since moving into the neighborhood during the summer.