Moscow offers to drop weapon plans if US keeps bases away from Russian territory.
The destroyer, which is set to stay in Havana for five days, took part in recent joint exercises with the Venezuelan navy and stopped in at former ally Nicaragua before sailing to Cuba.
It is accompanied by two supply ships.
The Chabanenko’s visit comes amid renewed diplomatic and economic relations between Cuba and Russia, which is increasing its presence in the Western Hemisphere amid rising tensions with Washington.
Some analysts believe Russia is signaling its unhappiness with US plans to build a missile defence system in eastern Europe and support for former Soviet republic Georgia in its recent conflict with Russia.
In public statements, US officials have placed little importance on the Russian naval visit to Latin America.
Russia was communist-run Cuba’s biggest benefactor before their alliance abruptly ended with the fall of the Soviet Union.
During the Cold War, the Soviet Union had a significant military presence in Cuba and Soviet warships were a common sight in Havana Bay.