The actor, who plays Jin-Soo Kwon in the hit series, was stopped by police at around 3 a.m. on Thursday in Honolulu, where the show is filmed.
Kim says in a statement: "I am deeply ashamed and embarrassed by the events of Thursday morning. It saddens me to know that I jeopardized the welfare of the kind people of Hawaii, a community that I love and call my home.
"It is my intention to cooperate fully with the police and I am grateful to them for their sensitivity throughout this matter.
"To my friends, family, colleagues and fans, thank you for your kind words of support. To those I have disappointed I can only ask that you accept my heartfelt apologies."
Kim's arrest marks the latest in a string of DUI-related incidents to plague the Lost cast in Hawaii--castmates Cynthia Watros and Michelle Rodriguez both pleaded guilty to driving under the influence in January 2007 and April 2008, respectively.
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