The report, from a news website run by North Korean defectors, said that senior officials were given the book as a gift in January.
North Korea has denounced the defectors as “human scum” and threatened to kill them.
Nazi leader Adolf Hitler wrote Mein Kampf in 1924 while in prison.
The book, which translates as My Struggle in English, outlines his early life and racist views.
News portal New Focus International wrote the original report, citing an unnamed North Korean official in China.
“Mentioning that Hitler managed to rebuild Germany in a short time following its defeat in WWI, Kim Jong-un issued an order for the Third Reich to be studied in depth and asked that practical applications be drawn from it,” the source reportedly said.
North Korea’s Ministry of People’s Security, which is responsible for policing, issued an angry response which was carried by the country’s official news agency, KCNA.
It dismissed the report as a “smear campaign” written by “a handful of human scum… moving desperately to deter [North Korea’s] progress”.
The defectors were being used by South Korea and the US, it went on.
The ministry was determined to “physically remove [the] despicable human scum who are committing treason”, the statement added.
The two Koreas remain technically at war after the 1950-53 Korean war ended with an armistice, not a peace treaty.
Ties between the two are currently very tense in the wake of Pyongyang’s 12 February nuclear test.
It is estimated that more than 20,000 North Koreans have defected to the South since the 1950s.
However, fleeing North Korea is dangerous, and defectors who are repatriated to North Korea face punishments including labour camps and execution, activists say.