The news comes just hours after the President was flown to a military hospital after the White House confirmed he was feeling "lethargic".
It was confirmed during the early hours of Friday morning that the President, 74, and First Lady, Melania, 50, had contracted coronavirus after coming in close contact with Trump's top aide, Hope Hicks, who also tested positive.
North Korean media reports the state leader to have said: "I have come across unexpected news that you and your commander have been tested positive for the coronavirus."
A translation of his message goes on to say: "I [send] consolation to you and your family.
"I sincerely wish you and your commander a complete recovery as soon as possible."
Kim adds: "You will surely get over it. Warm greetings to you and the commander."
The message was signed off with: "Chairman of the State Affairs Committee of the Democratic People's Republic of Korea, Kim Jong-un."
Trump has since taken to Twitter to share a video, filmed in The White House thanking American's for their support since his diagnosis.
He said: "I think I'm doing very well, but we're going to make sure things work out.
"The First Lady is doing very well, thank you so much - I appreciate it and I will never forget it."
Announcing his bombshell diagnosis on Twitter, Donald Trump said: "Tonight, @FLOTUS and I tested positive for COVID-19. We will begin our quarantine and recovery process immediately. We will get through this TOGETHER!"
It was confirmed by the White House that Trump had been taken to Walter Reed National Military Medical Centre in Maryland on Friday night and was to spend a "few days" there following advice from his medical team.
Trump's press secretary Kayleigh McEnany said that despite the President experiencing "mild symptoms" he remained in "good spirits".
She added: "Out of an abundance of caution, and at the recommendation of his physician and medical experts, the President will be working from the presidential offices at Walter Reed for the next few days.
"President Trump appreciates the outpouring of support for both he and the First Lady."
It's believed that Trump has also been treated with zinc, Vitamin D, famotidine, melatonin and asprin.
While unidentified sources told NBC that he was experiencing a low-grade fever.