Mr Hurst said nobody was injured when the World War II-era fighter crashed.
The Fire Service said it had vehicles and staff on stand-by at the show.
Thousands of the Focke-Wulfs were manufactured but it was a rare plane in New Zealand nowadays.
Further south, two people had minor injuries after a plane crashed on Otago's Tomahawk Beach this afternoon.
Police said the cause of that crash was not yet known but nobody other than the plane's two occupants was hurt.
A witness posted a picture of the crash on Reddit, saying: "This just cut out over my house in Dunedin. Lucky they made it to the beach. Both people survived!"
Police were at the crash scene near Dunedin.
The Civil Aviation Authority would investigate the Tomahawk Beach crash.