In 1982, Miura left the Shizuoka Gakuen High School after less than a year, and travelled alone to Brazil at the age of fifteen to become a professional footballer there. He signed with Clube Atlético Juventus, a youth club in São Paulo, and in 1986, Miura signed his first professional contract with Santos. He played for several other Brazilian clubs including Palmeiras and Coritiba, until his return to Japan in 1990.

In September 1990, Miura was named as part of the Japan squad for the 1990 Asian Games. At this competition, on September 26, he debuted against Bangladesh. After his debut, he played as a forward until 1997. In 1992, he played at the 1992 Asian Cup, which Japan went on to win. In 1993, in the 1994 World Cup qualification, he played thirteen games and scored thirteen goals. However, Japan failed to qualify for the 1994 World Cup. He also played at the 1994 Asian Games, the 1995 King Fahd Cup and the 1996 Asian Cup.

His time in Brazil elevated him to star status and on his return to Japan, he joined the Japan Soccer League (JSL) side Yomiuri SC, which later spun off from its parent company Yomiuri Shinbun and became Verdy Kawasaki with the launch of the J1 League in 1993. With Yomiuri/Kawasaki, Miura won four consecutive league titles playing alongside fellow Japanese national team regulars Ruy Ramos and Tsuyoshi Kitazawa. Yomiuri won the last two JSL titles in 1991 and 1992, and Verdy Kawasaki won the first two J1 League titles in 1993 and 1994. He was named the first J.League Most Valuable Player in 1993.

Miura then became the first Japanese footballer to play in Italy, joining Genoa in the 1994–95 Serie A season. In his Italian stint, he played 21 times and scored one goal, during the Genoa derby against Sampdoria. On 15 January 1994, Miura assisted Antonio Manicone’s match-winning goal against Padova. He returned to Verdy Kawasaki for the 1995 season and played with them until the end of the 1998 season. Miura made another attempt at playing in Europe with Croatia Zagreb in 1999. He returned to Japan, however, following a brief trial with Bournemouth, in the same year, and played with Kyoto Purple Sanga and Vissel Kobe, before eventually signing for Yokohama FC in 2005.

In 1997, Miura scored fourteen times for Japan during qualification for the 1998 World Cup, leading the Samurai Blue to their first ever World Cup finals. Despite this, Miura was controversially left out of the squad.

In February 2000, Miura played for Japan for the first time in two years. He played his last national team match later that year, and finished with the second-most career goals in Japanese national team history with 55 goals in 89 matches.

In 2007, Miura was selected for the 2007 J.League All-Star Soccer for J-East and played exceptionally well.

In 2012, and at the age of 45, Miura made his debut for the Japan futsal team in a 3–3 draw against Brazil. He came off the bench and was involved in the build up for the second goal scored by Nobuya Osodo. In his second appearance with the futsal team, he scored the third goal in a 3–1 win over Ukraine. In the 2012 Futsal World Cup, Miura appeared in all four matches for Japan, but failed to score as the Japanese were knocked out by Ukraine in the round of 16.

In November 2015, Miura signed a new one-year contract with Yokohama FC at the age of 48. In January 2017, Miura signed another new one-year contract with Yokohama, taking his professional career into his fifties.

On 5 March 2017, Miura became the oldest ever player to feature in a professional match when he started in Yokohama’s 1–1 draw against V-Varen Nagasaki. With 50 years and seven days, he surpassed the previous record held by Stanley Matthews from 1965 by two days. Seven days later, he broke Matthews’ record for oldest goalscorer in professional football when he struck the only goal of a 1–0 win over Thespakusatsu Gunma.

In January 2018, he signed a new contract, and renewed it again in January 2019, and January 2020. His most recent start came on 4 April 2019 against Avispa Fukuoka at the age of 52 years 37 days.

On 5 August 2020, he started in a J.League Cup match against Sagan Tosu, becoming the oldest player to take to the pitch in Japan’s league cup competition, at the age of 53 years, 5 months and 10 days. By doing so, he surpassed the previous record of 42 years, 10 months set in 2017 by Yukio Tsuchiya.

On 23 September 2020, he started in the J1 League match against Kawasaki Frontale and in doing so became the oldest player to take to the pitch in a J1 League match and the oldest player ever in a football match in the highest national division worldwide. Miura played 57 minutes in this match.