On March 17, 2013, Ryu recorded his first win as a Dodger, albeit, in a spring training game on St. Patrick's Day. He allowed just one run in 5⅔ innings, and retired the final 11 men he faced. He struck out six and allowed just five to reach base.
Ryu made his Major League Baseball debut in a start against the San Francisco Giants on April 2, 2013. He allowed 10 hits in 6.1 innings but only one earned run. Ryu picked up his first Major League win on April 7 over the Pittsburgh Pirates. On April 13 against the Arizona Diamondbacks, he recorded his first major league hit with a double in the third inning. He wound up 3 for 3 at the plate in the game, the first Dodgers pitcher to get three hits in a game since Randy Wolf in 2009. This game was also his 100th career win, in South Korea and the U.S. combined.
On May 1, 2013, Ryu pitched six innings against the Colorado Rockies and struck out 12 batters, his highest strikeout count in an MLB game so far.
On May 28, 2013, Ryu pitched a complete game shutout against the Los Angeles Angels of Anaheim, striking out seven batters, walking none, and conceding only two hits. It was the first shutout in Ryu's MLB career and the first shutout for a Korean-born pitcher since Chan Ho Park and Sun-woo Kim. In 30 starts with the Dodgers in 2013, Ryu was 14–8 with a 3.00 ERA. He was selected by Baseball America to their annual "All-Rookie team".
On October 6, 2013, Ryu became the first South Korean to serve as the starting pitcher of a Major League Baseball postseason game.
Ryu enjoys a popularity amongst South Korean baseball players, drawing South Korean fans as well as fans of Korean ancestry in nearly every stadium he pitches in. On July 22, 2013, after a 14–5 win against the Toronto Blue Jays played at Rogers Centre, several hundred fans of Korean ancestry stayed after the game to give Ryu a standing ovation, a common practice during the game, but a rarity for an ovation to occur after the game.