Sergei Shoigu said the flight engineer was extracted after a 12 hour mission by special forces on the ground in Syria.
He said: "The operation was successful. The engineer was delivered to our airbase, he is alive and well. I wanted to thank all our boys, who were working all night with great risk. At 03.40 am they completed their work."
British-based Syria watchdog Syrian Observatory for Human Rights has said it believes the Russian information to be true and that the airman is back at Russia's Hemeimeem air base, near the city of Latakia.
The Russian ambassador to France claimed the other airman - presumed to be the pilot - was wounded as he parachuted down and killed on the ground by "jihadists in the area".
According to a US official, the jet was hit inside Syrian airspace after briefly entering Turkish airspace.
The unnamed official told the Reuters news agency that the assessment was based on detection of the heat signature of the jet.
But Turkey's President Recep Tayyip Erdogan has repeated Turkey's claim that the jet was in Turkish airspace at the time it was hit in direct contradiction of the US analysis.
He said part of the damaged plane landed inside Turkey, injuring two civilians on the ground.
President Erdogan said on Wednesday that he has no "intention" of escalating the incident, which has triggered a major diplomatic confrontation.
"We are just defending our security and the rights of our brothers," he said, adding that no one should expect Turkey "to remain silent" when its border security was violated.
Turkish officials said two Russian planes approached the Turkish border and were warned before one of them was shot down, adding their information shows Turkish airspace was repeatedly violated.
NATO said the incursion into Turkish airspace lasted 17 seconds, but Moscow denies the plane ever entered Turkey, providing data of its own as proof.
Russia's president Vladimir Putin on Wednesday accused Turkey's leadership of deliberately supporting Islamification in its country and said Russia was sending its S-400 missile system to Syria to defend its airbase.
But, while speaking to reporters, the Russian ambassador to France added that Russia would be prepared to "create a joint staff" to fight the Islamic State in which Moscow would work with France, the United States and even Turkey.
The downing of the jet is the first time a NATO member's armed forces have shot down a Russian or Soviet military aircraft since the 1950s.