"We confirm with deep sadness the assassination of Ishaku Yakubi, a Monguno-based employee of Action Against Hunger, as well as of four other humanitarian workers", the aid group said in a statement.
The five Nigerian men were abducted by armed militants on 8 June, the Paris-based organization added.
The militants are believed to belong to Boko Haram, a violent Islamist insurgency active in the state of Borno, Cameroon, and Chad, according to the Nigerian online newspaper Premium Times.
The paper said that gunmen circulated the video of the execution-style shooting on social media. In the footage, they warn locals against working for foreigners, who they describe as "infidels".
For more than a decade, Boko Haram has been leading violent warfare targeting civilians in pursuit of eliminating the Western system of education and establish Sharia law in Nigeria. In 2015, the group pledged allegiance to the Daesh* terrorist organization.
* Daesh (aka ISIS/ISIL/IS/Islamic State) is a terrorist group banned in Russia and many other countries