Local media outlets report that the four policemen had fired live ammunition at protesters in Surulere area of the city.
Lagos State Governor, Babajide Sanwo-Olu, named the four policemen who he said are facing a disciplinary trial:
I am very sorry about this experience. All the erring officers involved have been arrested; Inspector Bagou Michael; Inspector Ekpoudom Etop; Sgt Nnamdi Majura and Sgt. Akinyemi
Benson and they are facing an orderly room trial immediately. https://t.co/a3HQhvhDXH
— Babajide Sanwo-Olu (@jidesanwoolu) October 15, 2020
Governor Sanwo-Olu also said that the state had established a 200m Nigerian naira ($521,000; £404,000) fund to compensate victims of police brutality.
The federal government has banned protests in the capital Abuja, citing public safety measures to tackle Covid-19.
Demonstrations against police brutality have taken place in cities across Nigeria in the past week. The protests have continued despite authorities agreeing to disband the Special Anti-Robbery Squad (Sars).
The unit has been accused of extrajudicial killings, extortion and torture, especially of young people.