The fight occurred at a popular brothel located in Simari area of Maiduguri.
Witnesses said the victim, Ibrahim Bulama, was shot dead by soldiers after they clashed over a woman at the brothel.
Air Force authorities confirmed the killing, but did not clearly admit its personnel were involved in a struggle for a prostitute.
The Commander of the 105 Composite Group, Charles Ohwo, an Air Commodore, told journalists at a press briefing on Thursday that the deceased was not shot.
He said the man died when soldiers were trying to retrieve a rifle allegedly snatched from their colleague.
According to the Nigeria Air Force account, the soldier, Kamal Usman, a Lance Corporal, was on his way home from his duty post when he ran into people having an argument.
He said the armed personnel was trying to find out what happened, when his rifle was snatched.
“Preliminary investigation revealed that, on Wednesday 7th December 2016, an airman, Lance Corporal Kamal Usman, left his duty post at about 10pm, and on his way home, when he came across some gathering near a hotel in Simari area; and in an attempt to find out what was wrong, the crowd got scared and took to their heels,” Mr. Ohwo said.
“When the airman decided to check the surroundings to find out what scared the crowd, he entered one room in the hotel and found a woman laying on a bed.
“Unfortunately, the deceased old man, Bulama mobilized some people and came back to the hotel and attacked him from the back with matchets, inflicting serious injuries on his head and snatched his rifle.
“On sensing danger, the lance corporal left and mobilized his fellow colleagues for assistance. Upon arrival at the scene, they descended on the old man, and beat him to death in the process of recovering their rifle.
“The airman is now recuperating at the air force medical facility in Maiduguri, while his colleagues who were involved in the incident have been detained pending further investigation,” Mr. Ohwo said.
Witnesses questioned the Air Force’s narratives, saying it did not explain what exactly took the armed airman to a brothel, or how exactly he got to see the woman on the bed, or what he was doing with her at the time the mob mobilised to attack him.
“The soldiers have to do their investigation very well, because all we heard was that a solder was attacked by angry mob after the old man was killed,” said a source who asked not to be named for safety reasons.
Journalists were ushered into the military clinic at the Air Force base where the accused airman, who had deep cuts on his head, was admitted. He was cuffed by the legs.
Mr. Ohwo called for calm, promising thorough investigation into the matter.