The 31-year-old was airlifted to hospital in Munich in a helicopter after the crash, police reported on Thursday. The 24-year-old driver of the tank was also lightly injured.
The crash happened in the mountainous Tyrol region of Austria, where the soldiers were on exercise on Wednesday evening. The driver reportedly lost his way in thick fog and the tank rolled over several times as it fell down the hill.
A recovery crane was brought in to the crash site, and only after it had recovered the tank could the two men be freed.