The Beech A23 plane had to make an emergency landing around 10:30 a.m. shortly after it departed the runway at Henderson-Oxford Airport along Huntsboro Road in Oxford.
The two people on board suffered non-life threatening injuries and were taken to Granville Medical Center. Their names and the extent of their injuries have not been released.
According to the Granville County Sheriff's Office, the 48-year-old plane developed engine problems about a half-mile south of the runway.
The Federal Aviation Administration is currently investigating the incident.
The FAA registry shows that the plane with the tail number, N3542R, is owned by Albert Wehe of Raleigh.