Spanish Prime Minister Mariano Rajoy said on Monday that eight French nationals and two Greeks were killed in the crash.
"It appears that there are two people who died and who have Greek nationality and eight French," he said during an interview with private television Telecinco.
The death of a ninth French national was confirmed by the ministry late on Tuesday morning. The man died in Madrid's La Paz hospital where he had been taken after the crash at a military base in southeastern Spain.
The two-seat F-16 jet "lost power" as it took off from the base near the southeastern city of Albacete and crashed into an area where other planes were parked, damaging five other aircraft, the defence ministry said in a statement.
Deeply saddened by the air crash in Spain – a tragedy which affects the whole NATO family. My heartfelt condolences. http://t.co/w9DLuIvfYC
— Jens Stoltenberg (@jensstoltenberg) January 26, 2015