Witnesses and the rights group Amnesty International said several people were killed and wounded when soldiers opened fire, BBC reported.
The state governor said about 25 people had been wounded but only one person had died.
An indefinite 24-hour curfew has been imposed on Lagos and other regions.
Protests over a now-disbanded police unit - the Special Anti-Robbery Squad (Sars) - have been taking place for two weeks, with demonstrators using the social media hashtag #EndSars to rally crowds.
As tensions continued to rise on Wednesday, police in different districts of Lagos fired shots in the air to disperse people defying the curfew.
The headquarters of the Nigerian Ports Authority was also set on fire, local media said.
Witnesses spoke of uniformed men opening fire in the wealthy Lekki suburb on Tuesday evening.
In a statement on Wednesday, President Buhari did not directly refer to the shootings, but called on people to have patience as police reforms "gather pace".
A statement issued by his office said the dissolution of the Sars was "the first step in a set of reform policies that will deliver a police system accountable to the Nigerian people".
Protests began nearly two weeks ago with calls for the Sars police unit, which had been accused of illegal detentions, assaults, and shootings, to be disbanded.
But the demonstrators called for more changes in the security forces as well as reforms to the way the country is run.
FA/PR
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