It is not clear when the footage dates from.
But the army says it was probably filmed in the north-east, where jihadists have been fighting for years.
An army spokesman described the violence shown in the video as a “dastardly act” that was against the core values of the Nigerian army.
Correspondents say the Nigerian authorities usually dismiss allegations of human rights abuses in the conflict against the Islamist militant group Boko Haram.
But in this case, the Nigerian army issued a strong statement of condemnation and promised the perpetrators would be tried and punished.
The military has also been under scrutiny for recent allegations that it detained thousands of children for suspected links to Boko Haram.
It has denied those reports, saying it treats children as “victims of war and not as suspects”.
Nigeria’s armed forces have been fighting Boko Haram in the north-east for the past decade. The authorities have said the group is “technically” defeated but it continues to attack military and civilian targets on a regular basis. BBC
