The video, titled a 'Message in Blood', shows several men in orange jumpsuits said to be captured Kurdish Peshmerga fighters, the BBC reported.
The victim is seen kneeling near a mosque in the IS-held city of Mosul before he is beheaded.
The jihadis warned that others will be killed if Kurdish leaders continue to back the US.
Backed by US air strikes, Peshmerga fighters from the autonomous Kurdistan region of northern Iraq have been trying to counter an advance by the IS.
On Thursday, a video posted online purportedly showed the aftermath of the killings of the Syrian soldiers - a long line of bodies of young men lying face down stripped to their underwear.
"The 250 Shabiha taken captive by the Islamic State from Tabqa in Raqqa have been executed," read the caption, using the name - Shabiha - given by the opposition to militiamen fighting for Syrian President Bashar al-Assad.
Tabqa air base, near the northern city of Raqqa, an IS stronghold, fell to IS Sunday after weeks of fierce fighting.
Last week, the IS drew worldwide condemnation after releasing a video showing the beheading of US journalist James Foley.
It said his death was in retaliation for US air strikes in Iraq, and the jihadi group threatened to kill other US hostages.
The IS has declared a "caliphate" across the parts of Syria and Iraq that it captured since June.