It happened around 10:30 in the 6400 block of Applecross Drive.
The victim told investigators she was sitting at a computer in her living room when she thought she'd been hit by lightning because it was stormy at the time.
She and a friend then spotted a bullet hole in a wall shared with an adjacent apartment.
Police identified the woman as 57-year-old Lillian Acala. Acala was taken to Cape Fear Valley Medical Center where she was listed in stable condition.
Police said they are looking for a person of interest who goes by the name "Champ" and is known to frequent the area of Applecross Avenue.
He is described as a black male between 25 and 30 years old. He is 5'8" – 5'9' and weighs between 200 and 225 lbs. He was last seen wearing a FUBU jersey and blue jeans. Police said he has unkempt hair and a beard.
Anyone with information is asked to call Crime Stoppers at (910) 483-TIPS (8477).