The frigate and submarine are part of a four-strong fleet that is due to arrive in Cuba on Wednesday.
The drills, by the submarine Kazan and the warship Admiral Gorshkov, involved firing high-precision missiles at mock enemy targets from a distance of more than 600km (370 miles), it said in a statement on Tuesday. The Admiral Gorshkov also conducted training in recent days to repel an air attack, the ministry said.
They are part of a group of four Russian vessels due to arrive in Cuba on Wednesday. Cuba said last week that such visits were standard practice by naval units from countries friendly to Havana, and that the ships carried no nuclear weapons and did not present a threat to the region.
The trip will nevertheless be closely watched by the United States at a time of acute tension with Russia over its war in Ukraine.
The US does not see the move as threatening, but the US Navy will monitor the exercises, a US official told reporters last week.
“This is about Russia showing that it’s still capable of some level of global power projection,” the official said.
Cuba, Russia strong bilateral relations
The Admiral Gorshkov is armed with new Zircon hypersonic missiles. The weapon has been designed to arm Russian cruisers, frigates and submarines and could be used against sea and ground targets.
Russian President Vladimir Putin has touted Zircon as a potent weapon capable of penetrating any existing antimissile defences by flying nine times faster than the speed of sound at a range of more than 1,000km (more than 620 miles).
The Admiral Gorshkov and the Kazan are accompanied by two support ships on their visit to Havana, which Cuban officials said reflected “historically friendly relations” between Russia and Cuba.
The Cuban Foreign Ministry said the Russian warships will be in Havana between Wednesday and June 17.
It is not the first time Russia has sent its warships to the Caribbean, but this week’s visit follows Putin’s warning that Moscow could respond to Ukraine’s Western allies allowing Kyiv to use their weapons to strike targets in Russia by giving similar weapons to adversaries of the West worldwide.