Trump and Kim had been due to hold high-stakes talks on June 12 aimed at ridding the reclusive state of nuclear weapons, but the meeting was recently thrown into doubt as both sides raised the prospect of scrapping the discussions and traded threats.
Trump's letter came a day after North Korea attacked US Vice President Mike Pence as "ignorant and stupid."
"Sadly, based on the tremendous anger and open hostility displayed in your most recent statement, I feel it is inappropriate, at this time, to have this long-planned meeting," Trump wrote in a letter to Kim released by the White House.
"Therefore, please let this letter serve to represent that the Singapore summit, for the good of both parties, but to the detriment of the world, will not take place."
Trump also brandished the threat of America's nuclear might in his letter, writing: "You talk about your nuclear capabilities, but ours are so massive and powerful that I pray to God they will never have to be used."
The US leader's letter appeared to leave the door open to a future meeting with Kim, however, stressing that he had been "very much looking forward to being there."
"We greatly appreciate your time, patience, and effort with respect to our recent negotiations and discussions" relative to the summit, he told Kim.
"I felt a wonderful dialogue was building up between you and me, and ultimately, it is only that dialogue that matters," Trump said. "If you change your mind having to do with this most important summit, please do not hesitate to call me or write.
"The world, and North Korea in particular, has lost a great opportunity for lasting peace and great prosperity and wealth. This missed opportunity is a truly sad moment in history."
The decision came as North Korea said it had "completely" dismantled its nuclear test site, in a carefully choreographed move portrayed by the isolated regime as a goodwill gesture ahead of the Singapore summit.
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