It happened around 7:25 p.m.at a private landing strip in the 3200 block of N.C. Highway 96 just north of Selma.
The plane's owner, Phillip Essey, of Laurinburg, told ABC11 that his daughter, 24-year-old Elaina Essey, of Greenville, was in the plane, a 1938 Piper J3 Cub, with an instructor. Essey said the plane was making an emergency landing when it hit power lines.
Essey said his daughter was taken to WakeMed but was not seriously injured.
The instructor's name and condition are unknown.
Neighbors report hearing a plane having engine problem just before the crash.
They said a man from the plane bandaged his own head and was banging on the window to get out after the crash, and the woman was moving her arms and legs.
The FAA will arrive Friday to investigate the crash.