The Korean-American lecturer had taught at Pyongyang University of Science and Technology (PUST) for several weeks prior to his arrest.
The investigation into Mr Kim was for matters "not connected in any way" to the university, PUST said.
Mr Kim was arrested just as he was about to leave Pyongyang. Authorities have not yet disclosed the reason.
According to South Korean news agency Yonhap, Mr Kim, who is in his late 50s, was involved in aid programmes and had been in North Korea to discuss relief activities.
The newspaper also said he was a former professor at Yanbian University in China.
PUST's chancellor, Park Chan-mo, was quoted by Reuters news agency as saying that Mr Kim "had been involved with some other activities outside PUST such as helping an orphanage".
Third US citizen held
The detention comes as tensions ratchet up in the Korean peninsula, with US warships steaming towards the region as Pyongyang threatens a "super-mighty pre-emptive strike".
The US has in the past accused North Korea of detaining its citizens to use them as pawns.
Mr Kim is one of three US citizens currently being held by North Korea.
In April last year, Kim Dong-chul, a 62-year-old naturalised US citizen born in South Korea, was sentenced to 10 years' hard labour for spying. He was arrested the previous October.
US student Otto Warmbier, 21, was arrested in January last year for trying to steal a propaganda sign from a hotel while visiting North Korea.
He was given 15 years' hard labour for crimes against the state in March 2016.