A number of people are reported to have been shot at a protest in Lekki, a suburb of the city.
A 24-hour curfew planned for Lagos, a key commercial hub and Africa's most populous city with an estimated 20 million residents, was delayed to allow commuters to return home.
Other regions are now imposing curfews.
Following reports of widespread violence across Nigeria, the city of Jos and Ekiti state said curfews would come into force later on Tuesday.
The southern Edo state imposed a curfew earlier, after officials said two police stations had been targeted, with attackers burning cars and stealing police equipment.
The protests began with calls for a much-hated police unit, the Special Anti-Robbery Squad (Sars), to be disbanded.
President Muhammadu Buhari did then dissolve the unit, which has been accused of illegal detentions, assaults and shootings, on 11 October.
But the demonstrators have called for more changes in the security forces as well as reforms to the way the country is run.
Lagos state Governor Babajide Sanwo-Olu has said that criminals have hijacked the protests "to unleash mayhem".
He said he had "watched with shock how what began as a peaceful #EndSARS protest has degenerated into a monster that is threatening the wellbeing of our society".
"Imposing this curfew was difficult, especially as we have just returned from a Covid-19 required lockdown," he wrote on Twitter.
"This curfew will allow security officials to immediately restore order to the state, arrest thugs and miscreants that have disrupted the peace."