Muto was born in Zama on November 7, 1988. After graduating from Ryutsu Keizai University, he joined J1 League club Vegalta Sendai in 2011. In March 2011, 2011 Tōhoku earthquake and tsunami occurred in wide area including Sendai. However Vegalta won the 4th place in 2011 and the 2nd place in 2012. In 2014, he moved to Urawa Reds. Urawa won the 2nd place in the 2016 J1 League. In 2017, Urawa won the champions in the 2017 AFC Champions League. Urawa also won the 2nd place in the 2019 AFC Champions League.