The Nigerian Air Force plane had reported engine failure, the military spokesman tweeted.
The plane was on the way to Minna, in the northern state of Niger to try to rescue 42 people who had been kidnapped.
The chief of air staff has ordered an immediate investigation.
In a series of tweets, the air force asked the public to "remain calm & await the outcome of investigation".
Air force spokesman Air Vice Marshal Ibikunle Daramola said that all those on board the small aircraft had died.
