The driver and another passenger were taken to hospital.
A Fire and Emergency New Zealand spokesperson said when crews found the car crashed in the creek, the passengers and driver had already made their way out of the vehicle.
It is understood police are investigating the cause of the crash.
Righteous is understood to be in a stable condition.
His role at Gloriavale is one of “servant” alongside Mark Christian, Maranatha Stedfast, Joshua Disciple and Michael Hope.
Servants sit beneath the overseeing “shepherd” - Howard Temple and other shepherds Noah Hopeful, Samuel Valor and Stephen Standfast.
Temple, 83, is currently before the courts on a raft of sex charges.
He is accused of indecently assaulting 10 girls across more than 20 years.
Court documents revealed Temple - who initially had name suppression and could not be identified publicly - of 24 charges of indecent assault involving 10 female complainants who were aged between 9 and 20 at the time.