The 1986 World Cup winner delivered the broadside at his first press conference as coach of Dubai-based club Al Wasl on Saturday, as he reflected on the recent FIFA presidential elections in which incumbent Sepp Blatter ran unopposed.
Blatter's main opponent, Mohamed Bin Hammam of Qatar, was suspended ahead of the vote along with fellow FIFA executive Jack Warner following accusations of bribery.
"There is a lot of corruption involving FIFA officials and they are all millionaires because of football," the former Argentina player and coach said.
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"I wonder if Blatter has ever kicked a football in his life, and yet we have been under the control of such people who have refused to give up power in FIFA.
"Why don't they all just relinquish their positions, take the money they have made and leave the running of the sport in the more capable hands of former football players?"
Maradona, a controversial figure who was sent home from the 1994 World Cup for using drugs, said he had never liked the FIFA establishment.
"I don't support corrupt people and I will never be on their side. I have always been asked by them to support the FIFA family. But what family are they talking about? This sport belongs to us and they have never ever asked us to be part of the development process," the 50-year-old said.
"They have too much power and this has made them so arrogant and proud. This is not what a genuine football lover needs from such officials. After all football, is the biggest sport in the world.
"We will continue doing what we are doing so that these corrupt people go away. They are too old and since they have made so much money at the cost of football, they should simply take it all and go away. Please leave football alone."
Maradona, who turned up more than an hour late for the media briefing, added that FIFA had stifled his attempts to form a players' union.
"What did FIFA do? They worked against us to ensure the union never saw the light of day," he said.
Meanwhile, FIFA is investigating Argentina's 4-1 defeat by Nigeria on Wednesday as part of a wider investigation into match-fixing, according to a report in Britain's Daily Telegraph on Saturday.
The paper said there was evidence of irregular patterns as referee Ibrahim Chaibou of Niger allowed three extra minutes of injury-time in addition to the five already awarded before Argentina scored from a penalty.
"FIFA can confirm that this match between Nigeria and Argentina was one that we had an active interest in, and forms part of a wider ongoing investigation," it said in a statement to the Telegraph.
The Nigerian Football Federation released a statement denying the accusation on Saturday.
"We are concerned at attempts by unscrupulous elements to play down the feat that our national team performed by beating Argentina," general secretary Musa Amadu said.
"This match was shown on many television stations, including ESPN, and in front of a crowd of 50,000, and we are certain that Nigeria's Super Eagles deservedly won that match, playing to the rules, and clearly outplaying our opponents."
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