The Supreme Leader's health is usually off-limits in a country where his image is firmly controlled by state media.
The country's main television channel has also shown footage of Mr Kim looking thinner than in recent years.
There have been persistent rumours about the North Korean leader's health in the decade he has been in power, but they have rarely been acknowledged by the country's notoriously secretive government.
What did North Korean viewers see?
Two recent clips shown on the country's main TV channel, Korea Central Television, have supposedly caused concern about the Supreme Leader's health.
One clip showed him arriving for a concert showing a dramatic weight loss.
The second - and most unusual clip - was of an unnamed Pyongyang citizen who told Central TV on Friday's main news: "Seeing [Mr Kim] become emaciated like that, we all became so sad.
"Everyone just started to cry," he said.
Earlier footage and photographs from Workers Party meetings this month hinted that Mr Kim was losing weight.
Analysis by the NK News website showed that the strap on his expensive designer watch was fastened tighter than at earlier events, suggesting that he was losing weight.
We still don't know why the video of the concerned citizen was shown. But Kwak Gil Seob, who heads One Korea Center, a website specializing in North Korea affairs, told the BBC that the Pyongyang regime "would never allow negative news around Kim Jong-un to be published" - meaning that the footage was aired "to show that Kim Jong-un is losing weight by himself".
The clip "shows that he is committed to his people", Mr Kwak said. "Kim Jong-un is using himself as a propaganda platform to emphasise the image of a leader working hard for his people day and night."