The soldiers were shown in front of the camera before extremists were seen sharpening their knives and killing four of them, according to Site Intelligence Group, a US website monitor.
The heads of the four young men were then seen on the ground, in the video said to have been filmed in the southern province of Shabwa.
The footage shows 10 more soldiers, blindfolded and crouching with their hands bound, being shot once each in the forehead, while another is riddled with bullets from behind.
According to Site, Al-Qaeda in the Arabian Peninsula (AQAP) has denied responsibility for the killings which took place in mid-April.
They were instead claimed by the "Shabwa Province" militia that has declared itself as a division of ISIS, a Sunni extremist group that has overrun swathes of Iraq and Syria.
In last week Following on from a declaration last week that ISIS had established a presence in war-torn Yemen, a group also affiliated with the network says it intends to post videos showing beheadings that have become the macabre trademark of the group.