Armed men are seen near burning tires on the street in Lagos, Nigeria. Reuters

The Nigerian army and police killed at least 12 peaceful protesters in two locations of Lagos in a deadly crackdown on demonstrations, Amnesty International said on Wednesday.

"Evidence gathered from eyewitnesses, video footage and hospital reports confirm that between 6:45 pm and 9pm on Tuesday 20 October, the Nigerian military opened fire on thousands of people who were peacefully calling for good governance and an end to police brutality," the group said in a statement.

Buildings were torched in Nigeria's biggest city Lagos on Wednesday as authorities shut down the economic hub after the shooting of peaceful protesters by security forces caused international outrage.

The Lagos governor at first insisted no fatalities had been recorded but later said the authorities were investigating the death of one person resulting from "blunt force trauma to the head".

He said at least 25 others were wounded.

A protester, who says his brother Emeka died from a stray bullet from the Army, reacts in Lagos. AP

Demonstrator Paul Sunday who was at the scene told reporters that the men who shot at the crowd were wearing masks and had army uniforms.

"They attacked us from back and from front," he said. "They came around 7pm when everywhere is dark."

Pictures and videos showing scenes of chaos in the aftermath of the shooting were widely shared on social media.

The shooting drew international condemnation, with UN High Commissioner for Human Rights Michelle Bachelet saying reports suggested it could have been premeditated.

"There is little doubt that this was a case of excessive use of force, resulting in unlawful killings with live ammunition, by Nigerian armed forces," she said.