Emergency services, initially concerned about fire, have now left the scene.
Warbirds Over Wanaka International Airshow general manager Ed Taylor told the Otago Daily Times he did not know what went wrong but was grateful no one was injured.
Some light aircraft have been able to take off on a shortened runway but there are still several other planes unable to leave.
Attempts are being made to move the crashed plane away from the runway using a truck with a crane hoist.