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 of Mali.
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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.
Called the "City of 333 Saints", Timbuktu around 1,000 kilometres northeast of Mali's capital Bamako, was attacked for months by jihadists.
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.
Born in Agoune, 100 kilometres west of Timbuktu, Faqi "was an active personality in the context of the occupation of Timbuktu," the ICC said in a statement.
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.