Kang Ki-young debuted in the 2009 play Our Bad Magnet. In 2012, he had a small role in the MBC medical sageuk The Horse Healer. He next landed a more significant role in the 2014 tvN workplace romantic comedy High School King of Savvy. In 2018, he was cast as Park Seo-joon’s best friend in the tvN romantic comedy What’s Wrong with Secretary Kim. That same year, he was named Best Supporting Actor at the MBC Drama Awards for his performance in the series My Secret Terrius. In 2019, he was cast in the disaster action comedy film Exit, in which he won the Best Supporting Actor trophy at the 8th Korea Best Star Award. He also scored a Best Supporting Actor nomination at the 28th Buil Film Awards for his work in the movie. In 2020, he collected three Best Supporting Actor nominations for the romantic comedy film Crazy Romance, which starred Kim Rae-won and Gong Hyo-jin.

In May 2019, Kang Ki-young and his non-celebrity fiancée tied the knot in a private ceremony after three years of dating.