Oh Young-soo began his decades-long acting career on stage in 1963. He has since appeared in more than 200 theater productions such as Crime on Goat Island, which won him Best Actor at the 1979 Dong-A Theater Awards. In 1994, he was named Baeksang Best Actor for Theater for Pigojigo Pigojigo. In 2000, he received another Best Actor citation from the National Theater Association of Korea for Abi. In 2006, he bagged the Best Actor honors at the Seoul Theater Festival for Jangpan.

Aside from his work in theater, he also has acting credits in both television and film, often as a monk. In 2021, he reached another milestone in his career when he became part of the widely popular Netflix survival drama Squid Game, which amassed a whopping 1.65 billion viewing hours on the first 28 days of its release. His performance in the series made him the first Korean actor to win the Golden Globe Award for Best Supporting Actor in a Series, Miniseries, or Television Film.