On arrival the Admiral Chabanenko destroyer fired a 21-salvo "international salute," which the country's coastal artillery returned.
The destroyer and two support ships will remain in Havana Bay until Tuesday.
Alexander Moiseyev, a counselor at the Russian embassy in Cuba, earlier said the visit "will help enhance the traditionally friendly ties between the armed forces of the two countries."
Russian Navy spokesman Igor Dygalo said the group command will meet with Cuban Navy officials, the mayor of Havana and Russian embassy staff.
The Russian sailors will lay wreaths at a monument to Cuban national hero Jose Marti and the Soviet Internationalist Soldier Memorial.
Cubans will also have an opportunity to visit the Russian ships.
The visit to Cuba completes a Caribbean tour by Russian battleships, which included stops in Venezuela, Panama and Nicaragua.
Russia announced last year that its Navy had resumed, and would continue, to build up a constant presence throughout the world.
Meanwhile, another Northern Fleet task force started a visit to Lisbon on Friday. After the visit, which will last until Monday, the group will sail through the Strait of Gibraltar, visit several ports in the Mediterranean, and take part in joint exercises with Russia's Black Sea Fleet.