Sheppard said in a tweet that the T-6 crashed a little before 2 p.m. local time near Lake Waurika, southwest of Hastings, Oklahoma.
In an update posted on Twitter Wednesday evening, Sheppard said that both pilots have returned to base. They were conducting a pilot instructor training mission at the time of the accident, Sheppard said.
An investigation is under way, the base said, and emergency crews are on the scene. Sheppard asked anyone who finds debris to not touch or move it, and instead to call the base at 940-676-2616.
The Air Force is fixing the problems with the T-6 Texan II that led to fluctuations in the oxygen concentration and caused hypoxia.
This is a breaking news story. It will be updated as events unfold.