The Russian Defence Ministry and the FSB security service were not immediately available for comment.
The 12-minute Russian-language video, released on the day Russia celebrates the anniversary of the 1945 victory over Nazi Germany with military parades, showed the man dressed in a black jump suit kneeling in a desert scene and urging other Russian agents to surrender.
"This idiot believed the promises of his state not to abandon him if he was captured," he said before a bearded man beheaded him with a knife.
The authenticity of the recording and the identity of the man could not immediately be verified, nor was it clear when the killing occurred.
The Russian defence ministry says about 30 Russian servicemen have been killed since the start of the Kremlin's operation there in September 2015.
(Reporting by Sami Aboudi; editing by Ralph Boulton)
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