"I can confirm a plane has crashed," a ministry spokeswoman said, with local media reporting that a Eurofighter jet went down near a military base at Albacete, 300 kilometres (180 miles) southeast of the capital.
The pilot died as a result of the accident, Spain's Ministry of Defence later confirmed.
Como consecuencia del siniestro, producido durante la maniobra de aproximación para el aterrizaje, ha fallecido el piloto del avión.— Ministerio Defensa (@Defensagob) 12 de octubre de 2017
The cause of the accident is being investigated and is still unknown, it added.
A Eurofighter last crashed in Spain in June 2014, killing the plane's pilot when it ploughed into grass short of the runway at the Moron air force base near Seville.
Spain's national day marks the date that Christopher Columbus first arrived in the Americas in 1492.
It falls this year in the middle of Spain's biggest political crisis in a decade as Catalonia's separatist leader is threatening to split the region from the rest of the country.