Witnesses say soldiers opened fire on demonstrators in Lagos on Tuesday evening after they gathered in defiance of a curfew and were blocking a major highway.
Amnesty International says it has “credible evidence” that protesters were killed.
The Nigerian Army responded by tweeting that no soldiers were at the scene.
The state government of Lagos says it will open an investigation into the incident and the state’s governor says he met victims of the shooting in hospital.
For two weeks, Nigeria’s government has struggled to calm protests against police brutality.
Demands include significant police reforms and the prosecution of officers accused of extortion, torture and extrajudicial killings.
At least 15 people have been killed since the protests began on October 8, according to Amnesty International.
