The Jeju United forward was involved in a crash with a taxi in the early hours of Monday morning and was arrested, an official at the Uijeongbu Police Station said.
The official said Kang and his friend who was also in the car will face further investigation.
Earlier this month, Kang received a six-month ban from the Korea Football Association (KFA) after testing positive for the anabolic steroid methyltestosterone. Kang blamed the failed test on a cream he used that helps grow a moustache.
The 28-year-old was set to win his first cap for the national team before news of the failed test in June having impressed with five goals in the opening weeks of the K-League campaign.