The May 28 airstrike was carried out on the outskirts of the militant group's de facto capital, Raqqa, on a command post where ISIS leaders were meeting, according to a ministry statement.
"According to information that is being verified through various channels, the leader of ISIS ... Abu Bakr al-Baghdadi was also present at the meeting and was killed as a result of the strike," the ministry said.
The United States confirmed that Russia conducted airstrikes on May 28, a US official said.
The Americans are investigating whether the strikes were in the precise area the Russians are claiming and whether there is any intelligence on who may have been in that location, the official said.
There have been previous reports of Baghdadi's death that later turned out to be false.
The Russian statement said the strike targeted ISIS leaders as they met to discuss their exit from the city. It said about 30 midlevel field commanders and up to 300 militants acting as bodyguards were also present.
The airstrike was carried out following drone footage confirmation of the meeting location, the statement said.
CNN senior international correspondent Clarissa Ward warned the details from the Russians were inconsistent with the typical behavior of ISIS leaders.
"They do not meet in big groupings like that because of drone strikes, because they are constantly being bombarded," she said.
"If he has been killed, of course it would deal a big blow to the group, but let's just look at the past few weeks -- we've had major terror attacks in London, in Baghdad, in Tehran, in Kabul. So clearly it is still business as usual for ISIS."
CNN military analyst Lt. Gen. Mark Hertling also warned against giving too much weight to Russia's sources.
"I'm not going to take this too seriously because there have been at least five reported killings of al-Baghdadi over the last three years," he said.
"I wouldn't believe the Russian sources based on anything they're hearing out of Syria."
An elusive and brutal leader
Officials have long described the ISIS leader as enemy No. 1 in the fight against ISIS
, and speculation has swirled over his whereabouts.
Baghdadi has kept a low profile, speaking out in occasional videos and audio messages
In a sermon at a Mosul, Iraq, mosque in 2014, he declared himself the leader of the Islamic caliphate. The sermon was filmed and widely watched around the world.
US forces captured him in Falluja, Iraq, in 2004. At the time, he was considered a low-level al Qaeda member.
He was freed in 2009, and within a year became the leader of Iraq's al Qaeda affiliate, heading up a renewed campaign of bombings and assassinations. Al Qaeda leaders later severed relations with him, saying he was insubordinate, killing too many civilians.
He earned a reputation for brutality as the leader of ISIS, which has seized and lost swaths of territory in Iraq and Syria.
The extremist group brought a reign of terror and intimidation into areas where they gained control. And the brutality has continued despite military setbacks. In one reported case, ISIS slaughtered 163 civilians and left their bodies in the street for days, the United Nations said.
Abu Bakr al-Baghdadi, which is a nom de guerre, was born Ibrahim Awwad Ibrahim Ali al-Badri al Samarrai.