The attack widens the circle of nations affected by the group's atrocities while showing its growth beyond a self-declared caliphate in Syria and Iraq.
The release of the 29-minute video comes a day after Afghanistan's president blamed the extremists for a suicide attack in his country that killed at least 35 people and underscores the chaos gripping Libya after its 2011 civil war and the killing of dictator Muammar Gaddafi.
It also mirrored a film released in February showing militants beheading 21 captured Egyptian Christians on a Libyan beach, which immediately drew Egyptian airstrikes on the group's suspected positions in Libya.
Ethiopia long has drawn the anger of Islamic extremists over its military's attacks on neighboring Somalia, whose population is almost entirely Muslim. While the militant in the video at one point said "Muslim blood that was shed under the hands of your religion is not cheap," it did not specifically mention the Ethiopian government's actions.
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The video, released via militant social media accounts and websites, could not be independently verified by The Associated Press. However, it corresponded to other videos released by the Islamic State group and bore the symbol of its al-Furqan media arm.
The video then switches between footage of the captives in the south being shot dead and the captives in the east being beheaded on a beach. It was not immediately possible to estimate how many captives were killed or confirm their identities.
In Ethiopia, government spokesman Redwan Hussein said officials were in contact with its embassy in Cairo to verify the video's authenticity. Hussein said he believed those killed likely were Ethiopian migrants hoping to reach Europe.