The protesters called on the government to end police brutality, after several years of complaints, with Amnesty International calling the latest death an "unlawful killing".
Thousands of messages of condolence and anger were posted throughout the day after a video showing the body of Kolade Johnson went viral.
Johnson was apparently hit by a stray bullet fired by police in broad daylight in Lagos.
"This is the price you pay for being a young Nigerian male not from a high-ranking family," wrote one of his neighbours @m_k_v_ng on Instagram.
He said he had never heard of the Nigerian police's Special Anti-Robbery Squad (SARS) firing "anyhow" in upmarket neighbourhoods of the financial capital.
"His blood is on your hands," he told the police.
The hashtag #EndSARS was created in 2016 by a group of human rights defenders.
One of them, Segun Awosanya, wants reform of the police and all special units to be disbanded, which he said have had military training and act with impunity.
"After a year of advocacy, things were better. The presidency stated that SARS elite squads must respond only to distress calls concerning house-breaking and kidnapping," he told AFP.
"But early January the new inspector general of police came in and we are back to square one.
"We've lost a lot of lives, police blatantly telling people at gun point, 'I will kill you and nothing will happen'. And guess what, nothing happens. We live under oppression."
Amnesty International has in recent years campaigned against police brutality and the use of torture in Nigeria, including by SARS units.
Its Nigeria director, Osai Ojigho, described Johnson as "the latest victim" of SARS, "which has become notorious for extrajudicial killings, torture and extortion".
"This appears to be an unlawful killing which must be impartially and thoroughly investigated, with any officers suspected of criminal responsibility for wrongdoing brought to justice in fair trial before an ordinary civilian court.
"It is shameful that more than two years since Amnesty International highlighted crimes under international law and human rights violations by SARS, these shocking incidents continue unabated."
