The video identified the slain man as the 19-year-old Mohamed Sa'id Ismail Musallam, an Israeli citizen of Arab descent, according to a CNN report.
The IS claimed in the video that Musallam was an Israeli agent, sent to infiltrate the militant group.
The family of the Israeli man had earlier denied that he was involved with the Israeli spy agency Mossad. Israeli officials declined to comment on Tuesday.
The video, posted on Tuesday on IS-affiliated social media accounts, shows a man, who appears to be Musallam, on his knees and wearing an orange jumpsuit. An adult IS fighter and a child -- both in fatigues -- stand behind him.
The adult, speaking in French, gives a command to the child to go forward with the killing.
The child then moves in front of the man and raises what appears to be a 9 mm semiautomatic handgun and shoots the victim in the forehead.
The victim immediately falls to the ground. The child appears to then fire at least two more shots into the victim's body.
The high-resolution video image appeared to match known images of Musallam, who had also been identified by the Israeli media.
His Israeli passport was shown in the video. The victim in the video spoke Arabic in a working-class Jerusalem dialect, consistent with the area, just north of Jerusalem, where Musallam was known to have lived.
An issue last month of IS's English-language propaganda magazine, Dabiq, included a purported interview with Musallam.
This was not the first time that the IS had used children to drive home its message.
An IS propaganda video released in January -- one that CNN could not independently verify -- showed a boy with a pistol apparently shooting two men.
Last August, a photo posted on Twitter from an IS stronghold showed a 7-year-old boy holding a man's severed head, and his father's words, "That's my boy".
IS has featured children as fighters before, calling them the "cubs of the caliphate" (the adult jihadis call each other "lions") and has encouraged foreign fighters to bring their families.
It has taken over schools to indoctrinate children. According to the Human Rights Watch, IS and other extremist groups "have specifically recruited children through free schooling campaigns that include weapon-training and have given them dangerous tasks, including suicide bombing missions".