Ahmad Al Faqi Al Mahdi was detained under an arrest warrant issued by the ICC last week and handed over by the authorities in Niger, the court said in a statement.
The details of his arrest were not immediately clear.
He is suspected "of war crimes allegedly committed in Timbuktu, Mali, between about 30 June 2012 and 10 July 2012, through intentionally directing attacks against buildings dedicated to religion and/or historical monuments," the statement said.
It is also the first case to be brought by the ICC -- the world's only permanent war crimes court -- for the unrest that has wracked the west African nation.
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Faqi "is expected to make a first appearance in the next few days, but an exact date has not been set," Abdallah said.
Faqi, a Tuareg leader also known Abu Tourab, is suspected of war crimes for deliberately destroying buildings at the UNESCO-listed desert heritage site in 2012.
In June 2012, Al-Qaeda-linked militants destroyed 16 of the northern city's mausoleums, dating back to its golden age as an economic, intellectual and spiritual centre in the 15th and 16th centuries.
Timbuktu mayor Halle Ousmane told AFP that Faqi's arrest was "good news".
"Destroying a mausoleum is like murdering someone, their history and their past," he said. "Like all people from Timbuktu I'm happy (about the arrest). I will closely follow the trial."
Faqi was a leader of Ansar Dine, a mainly Tuareg group linked to Al-Qaeda in the Islamic Maghreb (AQIM) and one of the groups that briefly took control of Mali's vast arid north in 2012.
In his role as part of the Islamic Court of Timbuktu, Faqi is alleged to have jointly ordered or carried out the destruction of nine of the mausoleums as well as the Sidi Yahia mosque.
The ICC said there were reasonable grounds to suspect that Faqi was "criminally responsible for having committed, individually and jointly with others, facilitated or otherwise contributed to the commission of war crimes" linked to the destruction of the buildings.