The 25-year-old was travelling to Spain from Morocco following Bayern's Club World Cup triumph last year along with the club's fitness coach Lorenzo Buenaventura, when the flight suffered heavy turbulence.
After the pressure in the cabin fell, Martinez said that he started "mentally" saying goodbye to members of his family.
"The truth is at that moment I feared for my life," Martinez told Sport1.de. "For 10 or 15 seconds I thought that was the end, that we were goners.
"At that point, I started mentally saying goodbye to my family. We were 13,000-16,000ft up, but luckily the pilot managed to regain control and perform an emergency landing, and there were no serious consequences."
Martinez moved to the Bundesliga outfit from Athletic Bilbao in 2012.