FC Tokyo As a child, Muto joined FC Tokyo's youth system, where he kept developing until 2010. He then enrolled in the Faculty of Economics of
Keio University but kept playing football, for Keio's team. Despite an injury which sidelined him, in his first season with Keio he won the "Rookie of the Year" title. In 2012 and 2013, FC Tokyo included him in their roster as a "Special Designated Player", an option that allows J-League clubs to field university players without a professional contract. However, he got on the pitch just once, at the end of a match in July 2013. In 2014, he signed his first professional contract with FC Tokyo and was given the shirt number 14. Coach Massimo Ficcadenti decided to use him from the first league round and, at the end of the season, Muto reached 33 appearances and scored 13 goals, matching the top debut record in the Japanese first division. At the end of the season, he was part of the J-League's Best XI. Muto graduated from Keio University in March 2015, and the following month was subject to a bid by
Chelsea. In April, he was elected as March's MVP (Player of the Month) in the J-League.
Mainz 05 On 30 May 2015, Muto joined
Bundesliga club
Mainz 05 on a four-year contract until 2019. On 31 October 2015, he scored a
hat-trick for the first time in his career and also became the second Japanese player after
Naohiro Takahara to score a hat-trick in the Bundesliga, in his team's 3–3 draw against
FC Augsburg.
Newcastle United Premier League club
Newcastle United announced on 27 July 2018 that they had reached a deal to sign Muto, pending him being granted a
UK work permit. He was granted the work permit on 2 August, officially becoming a Newcastle player on a four-year contract as part of a £9.5 million fee. Muto's first goal for Newcastle came in a 3–2 away loss to
Manchester United at
Old Trafford.
Eibar (loan) On 16 September 2020, Muto was loaned out to Spanish club
Eibar for the 2020–21 season.
Vissel Kobe On 7 August 2021,
Vissel Kobe announced that they signed Muto. ==International career==