After starting out at semi-professional club Gyeongju KHNP for half a year, Kim went on to play for Jeonbuk Hyundai Motors, where he won two K League 1 titles for two years before transferring to Beijing Guoan in 2019. After two-and-half years at the Chinese Super League, he joined Süper Lig side Fenerbahçe in 2021, and Serie A side Napoli in 2022. He was considered one of the best defenders in the world, when helping Napoli win a Serie A title in the 2022–23 season. Then, in July 2023, he moved to Bayern Munich for €50 million, making him the most expensive Asian player of all time.

Kim is a South Korean international, having progressed from under-20 onwards. He represented the national team at the 2022 FIFA World Cup and two editions of the AFC Asian Cup.