The air force said in a statement that its plane crashed near the Kaduna airport and that it was investigating the cause, Reuters reported.
The presidency said that in addition to the army general, other military officers died in the crash.
President Muhammadu Buhari, in a presidency statement, described the crash as a "mortal blow … at a time our armed forces are poised to end the security challenges facing the country."
The crash occurred three months after a small Nigerian air force passenger plane went down just outside the Abuja airport following what was said to be an engine failure, killing all seven people on board.
Nigeria, Africa's most populous nation, has had a poor air safety record in the past, although it has improved in recent years.
Buhari appointed Attahiru alongside other military chiefs in January after years of mounting criticism over spreading violence by terrorist groups and armed gangs.
RHM/PR