Choi Min-soo first forayed into acting in 1985 with the short film Eye and has since appeared in numerous movies and series. In 1989, he won Best New Actor for Film at the 25th Baeksang Arts Awards for Last Dance with Her. The following year, he picked up the Best Supporting Actor trophy at the 11th Blue Dragon Film Awards for the war drama Nambugun: North Korean Partisan in South Korea. In 1991, he starred in the MBC series What Is Love, in which he won an Excellence Award at the MBC Drama Awards. In 1993, he was named Best Actor for TV at the 29th Baeksang Arts Awards for his work in the MBC drama Walking Up to Heaven. In 1995, he took home another Best Actor for TV at 31st Baeksang Arts Awards for his performance in the hit SBS series Sandglass. He also received the Daesang at the 1995 SBS Drama Awards for the top-rating drama. In 1996 and 2000, he collected Best Actor honors at the Grand Bell Awards for the movies The Terrorist and Phantom: The Submarine. In 2001, he headlined the blockbuster film Libera Me, which earned him Best Actor at the 37th Baeksang Arts Awards. In 2004, he scored a Top Excellence Award at the MBC Drama Awards for Han River Ballad. In 2007 and 2014, he bagged Golden Acting Awards at the MBC Drama Awards for The Legend and Pride and Prejudice.

Choi Min-soo came from a family of actors. His father Choi Moo-ryong was a popular actor during the 1960s and 1970s while his mother Kang Hyo-sil was also an actress.  Additionally, his grandparents Jeon Ok and Kang Hong-sik were both well-known celebrities during their time. Choi married former Miss Korea contestant Elizabeth June Kang in 1994. They have two children together.

Choi Min-soo got involved in an assault case in 2008, resulting in his temporary leave from acting. In 2015, he withdrew from the KBS2 variety show A Look at Myself after punching the program’s production director. In 2019, he received a suspended sentence for retaliatory driving.