Video footage posted online by news website NU.nl showed the plane in free fall for several seconds.
The pilot of the plane that crashed ejected before impact and was not badly hurt, Dutch emergency services said. "Under the circumstances, he's doing well," said spokeswoman Brigitte Matter of the Menameradiel municipality.
There were no reports of injuries on the ground.
National broadcaster NOS showed footage of the plane, still burning, after it crashed near a house. It published a photo showing the second plane, also of the Swiss display team, with damage on its rear fin.
The cause of the crash, in the northern city of Leeuwarden, about 150 kilometres (90 miles) north of the capital Amsterdam, was unclear, the Swiss Defense Ministry said.
The Swiss plane, part of the Patrouille Suisse display team, had been due to take part in an air show this weekend. A new Joint Strike Fighter of the Dutch air force is due to make a first appearance at the international air show this weekend.
Get Breaking news, live coverage, and Latest News from India and around the world on NDTV.com. Catch all the Live TV action on NDTV 24x7 and NDTV India. Like us on Facebook or follow us on Twitter and Instagram for latest news and live news updates.