Concepcion Herrera, 48, and her 22-year-old son, Carlos, were found dead Thursday in their home in the 3600-block of W. 55th Place.
An autopsy found Carlos Herrera died of multiple stab wounds and his death was ruled a homicide on Friday. Autopsy results on his mother are still pending.
Police arrested the man at a home less than two blocks away from the crime scene on Friday afternoon. The victims' family said the man taken into custody is Concepcion Herrera's nephew.
A relative said that the nephew was hiding in a closet inside a home. Relatives said his mother asked about cuts on his body and that he responded by saying: "I did it. I did it."
Police said they received an unfounded 911 call on Thursday afternoon about an explosion at the home near Midway Airport. When police and firefighters arrived, there was a small fire and the two bodies were discovered.
Relatives said Concepcion was a homemaker and that her son Carlos had autism.
"He just was a good, sweet young man. He was very smart," said Marisa Manker, of Southside Occupational Academy.
"Carlos was just well-rounded and loved by many, really," said Carmella Bland, also of Southside Occupational Academy.
Chicago police will only say they're interviewing people.