The minor student who is below 16 years, identified as Z had circulated a photograph online, purportedly from the Prime Minister's Office (PMO) website, announcing the death of Lee on March 18, five days before he died in a hospital at the age of 91 of severe pneumonia.
The hoax message had prompted American broadcaster CNN and China's CCTV to put up erroneous tweets that Lee had died on March 18, which they withdrew later.
"The stern warning was administered in front of his parents. His identity has not been disclosed. The decision was taken after careful consideration of all relevant factors including Z's personal circumstances and readiness to accept responsibility, said the Attorney General's Chambers (AGC) in a statement.
The police have completed investigations into the case.
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"The culprit is a male Singaporean student below 16 years of age," the police said in a statement.
The young person was located by the police and interviewed. No hacking or unauthorised access of the PMO's took place, the statement added.
"Z shared the image with his friends. Within two minutes thereafter, he informed his friends the image was not an actual photo, but by then, the image had been forwarded by one or more of the original recipients," the AGC said.
"Z has been extremely contrite and deeply regrets the inconvenience and embarrassment his conduct has caused. He had cooperated fully with the police and explained the circumstances that led to his creation of the photograph," it added.