The plane had a flight instructor and student pilot on board.
The FAA says the plane was 10 miles northeast of Palm Springs when it dropped off the radar screen. The wreckage was located in Joshua Tree National Park.
The injured flyers were airlifted to Palm Spring hospitals. There is no word on the nature of their injuries.
The cause of the crash is under investigation. However, officials believe bad weather was an important factor.
The Associated Press contributed to this report.