Updated at 7:55 PM EST
They say crews were still looking for the man late Thursday afternoon, and signs indicate that he didn't survive.
The pilot's name wasn't immediately released.
Base officials say the pilot was six months into a training program at Luke, which is a major training base for the Air Force and foreign military services.
They say the crash occurred about 8:30 a.m. Thursday as the student pilot and an instructor in another F-16 were engaged in air-to-air combat training.
Authorities say the cause of the crash isn't immediately known.
BAGDAD, Ariz -- Officials say an F-16 fighter jet from Luke Air Force Base near Phoenix has crashed in northwestern Arizona.
There's no immediate word on the condition of the pilot after the crash Thursday in a military operations area near Bagdad in Yavapai County.
Luke officials said the jet was assigned to the 56th Fighter Wing.
Bagdad is about 85 miles northwest of the base located in suburban Glendale.
Luke spokeswoman 1st Lt. Tanya Wren said the cause of the crash isn't known and no other information was immediately available.
Yavapai County sheriff's spokesman Dwight D'Evelyn says the Sheriff's Office was contacted by the Air Force and has a helicopter looking for the crash site but hasn't found it yet.