Medvedev was welcomed in Havana by Cuba's Foreign Minister Bruno Rodriguez.
They are due to hold a press conference in the afternoon.
"Cuba and Russia have the highest level of exchanges and political dialogue, which has proved fruitful and useful," said the foreign ministry, which published a photo on its website of the two men meeting at Havana's airport.
Medvedev's visit comes at a crucial juncture for Cuba as it faces fuel shortages due to a US embargo -- first imposed in 1962 -- targeting ships transporting Venezuelan oil, Cuba's main supplier of crude.
Washington accuses Cuba of providing military support to Venezuela President Nicolas Maduro, whom the US is trying to oust in favor of his domestic rival Juan Guaido.
In recent weeks, hours-long queues have formed at service stations, the number of buses and trains running have fallen, air conditioning has been turned off in state companies and many state employees have been told to stay at home.
Pivotal importance
This crisis -- which the government says is "cyclical" -- underlines the importance of solidarity offered by allies China and Russia, whose Foreign Minister Sergey Lavrov visited the island in July.
"Russia's importance to Cuba has risen, both because of its status as a super power with the right to veto at the UN Security Council, and because it's a major producer of oil," said Arturo Lopez-Levy, a political analyst and professor at the Gustavus Adolphus College in Minnesota.
Russia's influence in Cuba waned with the break-up of the old Soviet Union three decades ago but it has been making a comeback.
Commercial exchanges increased by 34 percent in 2018 to $388 million and that figure should approach $500 in 2019, according to Russia's Deputy Prime Minister Yuriy Borisov.
But "Cuba needs to solve its economic imbalance and make progress with reforms in order to reduce its vulnerability," said political scientist Carlos Alzugaray, pointing to Havana having merely substituted the Soviet Union with Venezuela for its economic dependence.
'US irritant'
Moscow is third behind the European Union and China as Cuba's biggest trade partners.
In recent months it lent Cuba $40 million to help modernize the military industry and announced a plan to invest $1 billion between now and 2030 to renovate Cuba's rail network, as well as establishing agreements with Havana on nuclear power and cyber-security.
"The Russians are a lot more obvious about what they are trying to do -- that is to be an irritant to the United States," said Ric Herrero, executive director of the Cuba Study Group, which aims to foster relations between Washington and Havana.
For its part, China is also prepared to use Cuba to further its geo-political aims.
"The Chinese are advising the Cubans in technology, artificial intelligence, research, biotech, medicine," said Herrero.
"We know China has used and can use other countries' economic dependence on them as a political tool."
On Tuesday, China's ambassador to Cuba, Chen Xi stressed that "China is supporting and will always support... the Cuban people in their socialist efforts."
According to Herrero, the current outlook makes the Trump administration's bellicose approach to Cuba more questionable.
"Our current policy towards Cuba is not only isolating the United States from Cuba but also pushing the leadership in Havana towards the arms of our adversaries. This is completely counter-productive."