Abdul Rahman Mustafa Mohammed, also known as Abu Alaa al-Afari, was at a mosque near Tal Afar that was targeted, spokesman Brig-Gen Tahsin Ibrahim said.
There was no immediate confirmation from the US military or on IS media.
In recent weeks, there were unconfirmed reports that Afari had taken temporary charge of IS operations.
Iraqi sources claimed IS leader Abu Bakr al-Baghdadi had been incapacitated as a result of an air strike in Iraq in March.
Gen Ibrahim told the BBC that Afari was killed alongside dozens of militants who he had been meeting at the al-Shuhada (Martyrs) mosque in the village of al-Iyadhiya, near Tal Afar, where he was reportedly a well-known preacher.
Tal Afar, in the northern province of Nineveh, was seized by IS in June 2014.
The general did not specify which country carried out the air strike, but the US has been responsible for the vast majority since the coalition campaign began last August.
The ministry of defence separately published video purportedly showing the strike. It did not say when it took place, but one official told the Associated Press it was on Tuesday.
The Governor of Nineveh, Atheel al-Nujaifi, told the BBC in Washington that his contacts had confirmed Afari’s death.
A Pentagon spokeswoman said it had seen the media reports but did not have anything to confirm.
Yesterday, it announced that it carried out an air strike near Tal Afar in the past day, destroying a “militant fighting position and a heavy machine-gun”.
The Iraqi government has previously announced the deaths of IS leaders only for them to resurface alive.
But the BBC’s Ahmed Maher in Baghdad says that if Afari’s death is confirmed, it would represent another blow to IS, which has suffered a series of losses on the battlefield in recent months.