A court in the Iraqi capital of Baghdad found her guilty of "offering logistic support and help to (IS militants) in carrying out criminal acts".
Little is known about the woman, who was not named by the courts, but the spokesman of Iraq's Supreme Judicial Council said she was also found guilty of "distributing money" to IS militants in Mosul.
Abdul-Sattar Bayrkdar added that her husband had also been sentenced to death as a member of IS leadership.
The US have offered a reward of up to $25m (£18m) for information leading to the capture or death of Al Baghdadi, who remains one of Iraq's most-wanted fugitives.
He has been repeatedly reported as dead or seriously injured.