He crashed his car into a barrier between the road and pavement in July while giving three fellow skaters a lift back to their dormitory from a birthday party at the centre, Yonhap news agency reported.
South Korean Kim, a bronze medallist in the 1,500 metres at the last two Winter Games and a silver medallist in the team pursuit in Pyeongchang four years ago, was banned from competing for 18 months.
The length of the ban means Kim will be available to race at the 2026 Winter Olympics in Milan-Cortina.
"For an athlete, being banned for a year and a half can be career threatening," said Kim Seong-cheol, the head of the KSU's disciplinary committee.
"However, with Kim Min-seok, we did consider his track record of winning Olympic medals."
The head coach of the national speed skating team, Kim Jin-su, was suspended for a year for a failing to oversee the athletes in his charge properly.
Chung Jae-woong received a one-year ban for having driven the car earlier while under the influence of alcohol, but his brother Chung Jae-won, who won the team pursuit silver with Kim in Pyeongchang, was suspended for only two months.
"He didn't remember which car he rode back to the dorm in," Kim Seong-cheol added.
The car was driven inside the training centre and none of the four faces criminal charges.
