Rayshone McNeill, 31, turned himself in at the Wake County Detention Center.
The incident happened about 5:50 pm at Walapai Drive and Sippihaw Oaks Drive.
A 30-year-old woman was shot once in the leg, allegedly by McNeill, her boyfriend, and thrown from a vehicle.
Just before midnight, police said they found the suspect's BMW but were still searching for McNeil.
Police said he was possibly headed to Holly Springs or Willow Springs, where his most recent address is listed.
McNeill faces charges of assault with a deadly weapon inflicting serious injury and possession of a firearm by a felon.
Anyone with information about this incident is asked to call FVPD at (919) 552-3191.
NEED HELP FROM DOMESTIC VIOLENCE?
Some resource for those that may need help through Interact of Wake County:
24 Hour Crisis Hotline:
- Domestic Violence: (919) 828-7740
- Rape/Sexual Assault: (919) 828-3005
- Solace Center: (919) 828-3067
- Spanish Crisis Hotline: (844) 203-8896
- If you are in immediate danger please call 911.