The threat appeared as part of a message posted by ISIS members on social media.
George, who is the third-in-line to the British throne, had started his term at a primary school near the family's Kensington Palace home in central London last month.
According to the 'Star on Sunday', apicture was posted of George next to his new school Thomas's Batterseawith the caption "School Starts Early" on a popular ISIS channel on the secretive messaging service Telegram.
The newspaper said the post also featured words in Arabic which translate as - "When war comes with the melody of bullets, we descend on disbelief, desiring retaliation".
ISIS is known to favour Telegram because messages are encrypted and keep the user's location hidden.
The newspaper claimed its investigators discovered the message that seemed to target the young royal.
British intelligence officials are believed to be regularly monitoring the messaging service for ISIS activity.
Concerns about security at George's school have already been raised after a woman filmed herself wandering its corridors unchallenged days before term started.
Weeks later a woman was arrested at the school on suspicion of attempted burglary.
The Metropolitan Police had said it would be reviewing security arrangements at the school following the arrest.