A soldier who said he filmed the killing two weeks ago passed the recording to the Reuters news agency.
Nigeria’s security forces have repeatedly been accused of summary executions while fighting the militant Islamist group, Boko Haram.
The BBC has not been able to verify the video’s authenticity.
BBC Nigeria correspondent Will Ross says the video shows a man being pushed to the ground by a soldier, kicked in the head and then shot dead.
Next to him are at least four corpses, apparently of people who were also killed by soldiers.
An army spokesman said he had not seen the grainy video.
However, he believed it was staged and it was impossible for Nigerians soldiers to carry out such killings.
Earlier this month, rights group Amnesty International accused Nigeria’s security forces of carrying out widespread abuses in their campaign against Boko Haram, including extrajudicial killings, enforced disappearances and torture.
The group is campaigning to impose Islamic law across Nigeria.
It has carried out a wave of bombings and assassinations in northern and central Nigeria since 2009.
Maiduguri is one of the group’s strongholds.