Soldiers fired into the air and used tear gas and rubber bullets during the unrest in Tripoli, a security source said.
The man who died was in his 20s, the source said.
In a statement overnight, the army said soldiers were attacked during rioting in Tripoli. A fire-bomb was thrown at one of its vehicles and a hand grenade was hurled at a patrol, lightly wounding two soldiers, it said.
The army blamed the trouble on "a number of infiltrators" and called on peaceful protesters to quickly leave the streets.
Several banks were attacked during the protests and at least one was set on fire, a witness said.
Tripoli was the stage for big protests against Lebanon's ruling elite during countrywide demonstrations that erupted last October.
The banking association declared all banks in Tripoli shut from Tuesday until security is restored, saying banks had been targeted in "serious attacks and rioting".
Lebanon's banks have been a frequent target of protesters during the financial and economic crisis that has led to the collapse in the value of the Lebanese pound and frozen savers out of their deposits.
The long-brewing crisis came to a head last year as capital inflows to Lebanon slowed and protests erupted against its political elite. Since then, the pound has lost more than half its value, fuelling inflation in a country heavily dependent on imports.
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