Speaking at the UN, Mrs Clooney said IS had declared it will "destroy" the country's Yazidi ethnic group through murder, rape and forced conversions.
The British-Lebanese human rights lawyer said IS was also attacking Christians, and Shia and Sunni Muslims.
Mrs Clooney, who is based in London, accused the UN of "inaction".
She said: "The UN was created as the world's way of saying 'never again' to the genocide perpetrated by the Nazis.
"And yet here we are, 70 years later, discussing the UN's inaction in the face of a genocide that we all know about, and that is ongoing."
The UK is drafting a Security Council resolution to establish a UN investigation, but Mrs Clooney said the Iraqi government needs to send a letter formally requesting the inquiry before the 15-member council can vote.
Mrs Clooney called for mass graves to be preserved and exhumed, and witness evidence to be recorded, even if it was not supported by Iraqi Prime Minister Haider al-Abadi, who was present at the UN meeting.
Mrs Clooney said the organisation should press ahead regardless.
She ended her speech to the UN by saying: "Don't let this be another Rwanda, where you regret doing too little, too late. Don't let Isis [Islamic State] get away with genocide."
Who, What, Why: Who are the Yazidis?
Mrs Clooney, a barrister at Doughty Street Chambers, appeared at the UN in New York to represent victims including Yazidi genocide survivor Nadia Murad.
Ms Murad told UN members: "I can't understand why you are letting IS get away with it."
Last year, the UN accused Islamic State for the first time of committing genocide against Yazidis in Iraq and Syria.
A report said IS had subjected captured Yazidis to the "most horrific of atrocities", killing or enslaving thousands.
At least 3,200 Yazidis were being held by IS, the report stated.

The raids came a day after it emerged a Frenchman was being held by police investigating the murder of three people at the Brussels Jewish Museum.
Mehdi Nemmouche, 29, was arrested at a station in Marseille on Friday.
Prosecutors say he has claimed responsibility for the attack and spent more than a year in Syria.
Interior Minister Bernard Cazaneuve told Europe 1 radio on Monday: "There are people who recruit jihadists. There are as I'm speaking arrests being made."
"We are acting everywhere. There will be no respite in the fight against terrorists."
There is no suggestion of a link between the four arrests on Monday and the detention of Mr Nemmouche during a random check on a coach arriving from Amsterdam in southern France on Friday.
But Mr Nemmouche is said to have had links with radical Islamists and served five years in jail in France for robbery before being released in December 2012.
When he was arrested, he had with him a Kalashnikov rifle and a handgun believed to have been used in the attack, the Paris prosecutor said.
He was also said to have had a white sheet emblazoned with the name of the Islamic State of Iraq and the Levant, a jihadist group fighting in Syria, and a camera with a 40-second video showing the two guns and a voice recording, claiming responsibility for the killings.
Speaking on French radio station RTL on Monday, the head of French Jewish association CRIF, Roger Cukierman, called for more resources to be given to the foreign intelligence service, the DGSE, to track militants returning to France from Syria.
He feared "they would become 700 time bombs when they return", referring to the estimated number of French-born jihadists in Syria.
Belgium has requested Mr Nemmouche's extradition from France and police have to decide whether to extend his detention until Thursday.
Three people died when a gunman opened fire at the museum in the busy Sablon area of the Belgian capital on 24 May. They were an Israeli couple in their 50s, and a French female volunteer.
A Belgian man, believed to be an employee of the museum, was critically injured.
Lawyer Amal Clooney has urged the UN to act against so-called Islamic State by backing a UK-led investigation into the group's atrocities in Iraq.
[NEXT_CONCEPT]
Four people have been arrested in the Paris region and southern France, officials say, on suspicion of recruiting militants to fight in Syria.