The Eurofighter jet exploded shortly after 2pm shortly after take-off for a routine practice mission, Spanish daily ABC reported.
A ministry of defence spokesperson told Spain's Europa Press news agency the pilot had died in the accident.
The ministry is now investigating.
The Morón Air Base is about 60km (37 miles) from the Andalusian capital of Seville. It is key to US operations in the Mediterranean.
It is shared by Spain and the US Air Force, but only Spain operates the Eurofighter jet.
Defence group BAE builds the fighter jet with European aerospace group Airbus and Italian defence contractor Finmeccanica.
The Eurofighter consortium, Europe's largest defence programme, is in fierce competition with other fighter-jet makers such as Lockheed Martin, Boeing and Dassault Aviation.