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.