A Pentagon spokesperson, Marine Maj.
According to the New York Times, the militants were caught by the Iraqi military in cooperation with the American intelligence operation in Syria and Turkey.
The result of the three-month operation to capture the terrorist leaders, who had been hiding in Syria and Turkey, represents an important victory for the Iraqi and U.S. intelligence agencies.
Baghdadi, who declared himself ruler of all Muslims in 2014 after capturing Iraq's main northern city Mosul, is now believed to be hiding in the Iraqi-Syrian border region after losing all the cities and towns of his self-proclaimed caliphate.
Earlier this month, the coalition announced a drive to clear the final pockets of ISIS territory inside Syria.
"Only that captured the five most wanted leaders of ISIS", he said on Twitter, without specifying details.More news: Syrian army fires missiles into Golan Heights for first time in decades
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ISIS leader Abu Bakr al-Baghdadi was not one of the men captured - who now has a $25million bounty on his head from the US State Department.
The official, who spoke on the condition of anonymity, said: "His movements are discreet and he never travels in a convoy".
In a statement on Thursday, coalition spokesman Army Col. Ryan Dillon called the arrest a "significant blow" to ISIS terror group.
The militant group swept into Iraq in the summer of 2014, taking control of almost a third of the country.
Islamic State militants last month restated their loyalty to Baghdadi, in what is believed to be their first public pledge of allegiance to him since his self-proclaimed caliphate in Syria and Iraq collapsed a year ago.
With the group's physical caliphate now largely destroyed, anti-ISIS operations are increasingly focused on targeting the militants' remaining leadership.