The bodies of Barzan Umar Ahmad and his wife Sazane Ismail Abd Allah, who also works at the Red Crescent, were discovered late on Friday on a street in the Hay al-Intisar district in the northern city of Mosul, said Red Crescent official Hawar Faris on Saturday.
Their car appeared to have come under heavy gunfire.
Iraq has descended into chaos in recent days, with a spate of attacks and kidnappings targeting foreigners.
Three Japanese, a Palestinian and a Canadian of Syrian origin have been kidnapped in Iraq this week. All of them, except for one Japanese who is a freelance photojournalist, are all aid workers. A Briton is also missing. Seven Korean pastors had also been taken hostage but were quickly released.