Natasha Hubbard, 36, has been charged with aggravated assault.
Authorities said 29-year-old Adriana Miranda was pushing her child in a stroller on Boyd Street in the Toy District at about 1 p.m. on Thursday when Hubbard unbelted the child and grabbed him by the leg.
According to witnesses, Hubbard swung the boy over her head and slammed him into the metal rail of a truck.
LAPD Lt. Paul Vernon said Miranda and her sister fought off the woman and were able to grab the baby back.
Hubbard then allegedly attacked Miranda, who was holding her child. They ran into a store for protection, but the store kicked them out.
Officers arrived, found Hubbard and arrested her.
"Back at the police station, she told one of my detectives that she had done this because she wanted to break the child's arm off and eat it," Vernon said. "That can give you some idea where her mind is or what's in her mind."
Authorities say the child was bruised but is expected to be OK.
Police say Hubbard has an extensive criminal history, and they want to see if she was acting strangely in an aggressive way to others in the area last week.
Anyone with information related to the incident or the suspect should contact the Los Angeles Police Department at (877) LAPD-24-7.