According to the ministry, the Israeli F-16 jets carrying out the strikes used the Russian plane as a cover to allow them to approach their targets on the ground without being hit by Syrian anti-aircraft fire.
A recovery operation in the Mediterranean Sea is underway, Konashenkov said.
Foreign powers involved in the conflict - including Israel and Russian Federation - operate hotlines to exchange operational details to avoid one side accidentally attacking the other's forces.
Russia, the biggest outside backer of Syrian President Bashar Assad in his fight against rebels, has been preparing for an offensive on the city of Idlib, which is controlled by rebels and now home to about 3 million people.
A Russian Defense Ministry spokesman said Israel had given a warning, but it came less than a minute before the airstrikes - not enough time for the IL-20 to take evasive action. "As a result, the Ilyushin-20, its reflective surface being far greater than that of the F-16, was downed by a missile launched with the S-200 system", Konashenkov told reporters.
"On September 17, at about 11:00 PM Moscow time, the connection with the crew of the Russian Il-20 aircraft was lost over the Mediterranean Sea when the plane was returning to the airbase of Khmeimim, 35 kilometers from the Syrian coast", the official said.
In a highly unusual move, the IDF directly acknowledged the Israeli strikes, revealing the target was a Syrian Armed Forces facility utilized to manufacture "accurate and lethal weapons" that "were about to be transferred on behalf of Iran to Hezbollah in Lebanon".
In March this year, a Russian military transport plane crashed when coming in to land at the Hmeymim base, killing all 39 people on board.
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The Russian Foreign Ministry summoned Israeli Ambassador Gary Koren over the incident, and Russian Defense Minister Sergei Shoigu told his Israeli counterpart, Avigdor Lieberman, that Israel was responsible.
It sees Iran's military presence in Syria as a threat, and Prime Minister Benjamin Netanyahu told Putin by phone on Tuesday his forces would keep acting against it.
"Putin pointed to the fact that the Israeli air force has been conducting operations in breach of Syria's sovereignty".
Israel has refrained from taking sides in the Syrian civil war. Gen. Ronen Manelis said in a statement that Israel "expresses sorrow for the death of the aircrew members of the Russian plane that was downed tonight due to Syrian anti-aircraft fire", Haartz reported.
Russia, Turkey and Iran have declared four de-escalation zones around Syria since a year ago, all of them but Idlib ended in a military offensive and deals in which the rebels surrendered.
"By Oct. 10, at the suggestion of the Turkish president, (we agreed) on the withdrawal from that zone of the heavy weapons, tanks, rockets systems and mortars of all opposition groups", Putin said, with Erdogan standing alongside him.
"I think it will impose very serious restriction on Israel's freedom of activity", she said.
Russian President Vladimir Putin struck a more measured tone at a press conference Tuesday, saying that "it looks like a string of tragic circumstances".