The video documented an execution that reportedly happened shortly after the jihadist group captured the city on May 21.
It shows the soldiers in green and brown military uniforms being shot dead on the amphitheatre's stage in front of an enormous version of the group's black and white flag.
The executioners all appear to be children or teenagers and are wearing desert camouflage and brown bandanas.
The killings are carried out in front of a relatively sparse crowd of men and some children watching from the ancient theatre's seats.
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The executions in the Palmyra amphitheatre were first reported on May 27 by the Syrian Observatory for Human Rights, a Britain-based monitor, less than a week after IS captured the city.
At the time, Syria's antiquities director Mamoun Abdelkarim said he feared the killings could signal the start of "the group's barbarism and savagery against the ancient monuments of Palmyra".
"Using the Roman theatre to execute people proves that these people are against humanity," he told AFP.
So far, IS is not reported to have damaged the actual ruins, although it has blown up and desecrated Muslim graves in the city and destroyed a statue outside the Palmyra Museum.
IS has regularly released videos of its mass executions, with slick production and gruesome violence that experts say is a key propaganda tool for the group.