More than 500 people, including high-ranking intelligence and police officials, are thought to have died when the 23-storey building crumbled in the capital, Pyongyang.
Kim was reportedly unable to sleep after learning of the tragedy last week, thought to have been caused by poor workmanship.
According to a Japanese newspaper with sources in North Korea, the key officials and engineers behind the building of the apartment complex have been rounded up and handed down deadly or severe punishment.
Four design and construction engineers were executed by firing squad and a military official in charge of the project was sent to a prison camp, a source told the Tokyo Shimbun newspaper.
The Japanese newspaper said that although the exact cause of the accident remains unclear, shoddy construction is likely to be the cause because on-site directors and workers often smuggle away steel and cement to sell on the black market.
Another Japanese newspaper, Yomiuri Shimbun, reported that the building was inhabited by top intelligence and police officials, which might account for Kim Jong-un's wrath.
