The airstrike took place in the Iraqi town of Barwanah, in Anbar province, the statement said.
Adnani was first moved to the city of Hit for treatment after "losing a large amount of blood." He was then transferred to Mosul under tight security, according to the statement.
When pressed for details on the reported Iraqi airstrike, a spokesman for Iraq's Joint Operations Command said authorities have been chasing Adnani and following his movements for more than a month.
He said the terror leader was given two bags of blood to help stabilize his medical condition.
Iraqi state television also reported that Adnani had been hurt.
While Abu Bakr al-Baghdadi, as the caliph of the Islamic State in Iraq and Syria, has been the terror group's unquestioned leader, Adnani has been perhaps its most public figure, having made several audio recordings. He has been floated as its next leader
should something happen to Baghdadi.
The U.S. State Department officially labeled Adnani a terrorist
in August 2014. That designation characterized him as "the official spokesman for and a senior leader" of ISIS, a position he obtained after becoming "one of the first foreign fighters to oppose (U.S.-led) coalition forces in Iraq."
Between 2005 and 2010 during the Iraq conflict, Adnani was captured and spent time in custody, including, it is believed, at the U.S. detention facility, Camp Bucca.
In May of this year, the State Department announced a reward of up to $5 million for information leading to Adnani
, who was born as Taha Sobhi Falaha in Syria.
That statement noted his "repeated calls for attacks against Westerns and (his having) vowed 'defeat' for the United States."
In June 2014, Adnani was the first to declare a "caliphate" for parts of Syria and Iraq indicating ISIS' aim of not just being a terrorist group, but a governing entity.
Yet he was also vocal in calling for attacks outside the region, including his assertion that ISIS supporters in the West have a religious duty to launch lone-wolf attacks. Adnani renewed that call -- which analysts characterized as a game changer, not to mention a possible inspiration for ISIS-inspired attacks in North America, Europe and Australia -- in January.