It happened Monday night on the 1200 block of Gordon Street near Fountain Avenue.
Authorities said the suspect banged on the neighbor's door. When two women opened it, he attacked them.
A woman in her 60s was stabbed in an eye. She was hospitalized for surgery.
A 24-year-old woman was stabbed in her left hand and also taken to a hospital. Her 3-year-old son was not injured and is in protective custody.
Both women are in stable condition.
Detectives said the suspect suffered a knife wound to his shoulder.
The incident was under investigation.