Mr Erdogan said Russia had no right to "slander" Turkey with such claims.
Russia and Turkey have been locked in an angry dispute since Turkey shot down a Russian jet last month.
Russian President Vladimir Putin had already accused Ankara of downing the plane on its Syrian border to protect oil supply lines.
"According to available information, the highest level of the political leadership of the country, President Erdogan and his family, are involved in this criminal business," Mr Antonov told journalists in Moscow.
"The Turkish leadership has demonstrated extreme cynicism. Look at what they are doing!" he said.
"They have invaded the territory of another country and are brazenly plundering it."
The Russian defence ministry does not usually invite foreign journalists to its media briefings on Syria. But on Wednesday it made an exception.
It had a message it wanted the whole world to hear: that the faces of Turkey`s leaders, including President Erdogan, were "smeared with stolen oil".
Invited journalists and military attaches were shown satellite images and grainy video footage, purporting to show tanker trucks with oil crossing from IS-held territory into Turkey.
But, from what I could tell, no evidence was presented to implicate the Turkish president. He has accused Russia of slander.
After the shooting down of the Russian bomber by Turkey last week, the war of words continues between Moscow and Ankara.
Listening to the military officials at this briefing, you could hear the anger in their voices. Their strong language reflects their president`s conviction that Turkey has "stabbed Russia in the back".
The defence ministry cited satellite images that it said showed oil tankers travelling from IS-held territory to Turkey.
The trucks, it said, travelled to three locations - including refineries - in Turkey and some was then moved on to a third country.
Russia said it was producing only "part of the evidence" for now and did not provide direct proof of their claim that Mr Erdogan and family were involved.
Responding to the Russian allegations, Mr Erdogan said "no one has a right to engage in slander against Turkey by saying that Turkey is buying oil from Daesh [IS]".
He repeated a promise to resign if the claims were proven true, but added he did not want to see relations with Russia worsen further.
US officials have previously said they have information suggesting Turkish "middlemen" were involved in the illegal IS oil trade.
The Turkish authorities have made commitments to tackle smuggling on their territory.Despite the tensions, Russian Foreign Minister Sergei Lavrov has said he is prepared to meet Turkish counterpart Mevlut Cavusoglu at a conference in the Serbian capital Belgrade this week.
Mr Lavrov said he was willing to "hear what Mr Cavusoglu has to say", in comments broadcast on the Rossiya 24 news channel.
It would be the first time the men have met since the downing of the jet.
Turkey said the Russian SU-24 fighter plane intruded into its airspace and ignored repeated warnings to leave.
Funeral ceremonies have been taking place for Oleg Peshkov, the plane`s pilot who Russia said was shot dead after parachuting from the jet.
Russia and Turkey have important economic ties, and in the wake of the incident Moscow imposed visa requirements for Turkish visitors, and placed restrictions on trade with Ankara.
More about:
