Kubo began his professional career with the Chiba Lotte Marines of Nippon Professional Baseball. He made his NPB debut on April 2, 2005. Kubo then went on to play for the Marines through the 2008 season.
In 2009, Kubo joined the Hanshin Tigers of NPB. He played for the team in the 2009, 2010, 2011, 2012, and 2013 seasons before becoming a free agent after 2013.
Kubo joined the Yokohama DeNA BayStars of NPB for the 2014 season. He played for the team through the 2017 season before becoming a free agent at the end of the year.
On April 19, 2018, Kubo signed with the Gary SouthShore RailCats of the American Association of Independent Professional Baseball. He was released by Gary on May 11, but re-signed on June 28.[1] In 3 games with Gary, Kubo recorded a 4.05 ERA with 4 strikeouts in 6+2⁄3 innings.
On July 13, 2018, Kubo was traded to the Sugar Land Skeeters of the Atlantic League of Professional Baseball.[2] He finished the year with the Skeeters, pitching in 13 games and posting a 5–2 record and 5.14 ERA. He became a free agent after the season.
On April 3, 2019, Kubo signed with the Bravos de León of the Mexican League.[3] He spent the 2019 season with the club and logged an 8-14 record and 5.98 ERA while leading the league with 154 strikeouts. Kubo was released on January 13, 2020.[4]
On December 25, 2022, Kubo signed with the Hamburg Stealers of the German Baseball Bundesliga for the 2023 season.[5][6] Kubo finished the season with 122 innings pitched, 104 strikeouts and an ERA of 1.62, leading the Bundesliga Nord in the former two stats, and ERA with a minimum of 35 innings pitched, winning the Best Pitcher Award of the Bundesliga Nord.[7]
On March 17, 2025, Kubo signed with the Hyogo Bravers of the Sawakami Kansai Independent League in Japan.[8]