The shooting happened about 2 a.m. on Saturday near the city of Globe and the San Carlos Reservation in central Arizona.
The FBI said U.S. Forest Service and San Carlos Apache Tribal police officers shot at the suspect after encountering the man, who opened fire first.
The man, whose identity is pending family notification, died and no officers were hurt.
Authorities believe he's the same man who shot at a forest service fire prevention officer in Forest Lakes on July 4 and had been linked to multiple brush fires that were intentionally set around that time.
The FBI is leading the investigation because of the assault on federal officers.