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.