Police spokesman Sgt. Sammy Morris says the child and the woman died at hospitals after the crash Thursday night.
The woman was identified as 29-year-old Sharice Swain, of Cleveland. Her death is being investigated as a homicide.
The child's name hasn't been released by the coroner.
Police say the woman was stabbed during the argument and then drove off. It's unclear if she was trying to hit her attacker's daughter in retaliation.
Police say the girl's mother was taken into custody, but there is no word on any charges.