Miyaichi has represented Japan from under-15 to under-19 level. He took part in the 2009 U-17 World Cup as a member of Japan U-17 national team. He played 2 matches at the tournament.

Miyaichi was born into a sporting family. His brother, Tsuyoshi, was also a football player; and his father, Tatsuya Nomoura, was a basketball player who played for and later managed the Toyota Motors basketball club. Miyaichi started playing football in his elementary school years at Sylphid F.C. in Nagoya. He entered Chukyo University Chukyo High School and played for the school football club. In the 2010 season, the team advanced to the All Japan High School Soccer Tournament but were defeated in the first round in a match televised across Japan.

During his trial at Arsenal in the summer of 2010, Miyaichi impressed the Arsenal manager, Arsène Wenger, signing a professional contract on 31 January 2011. Wenger said: “We’re delighted that Ryo Miyaichi has joined us. He trialled with us in the summer and has raw ability which has attracted many clubs around the world”.

Just after he signed for Arsenal, it was announced that he was set to join Feyenoord on loan. On 5 February, in his first appearance for Feyenoord, he played the full 90 minutes against Vitesse Arnhem in a 1–1 draw, and was named man of the match. Miyaichi then played against Heracles Almelo where he scored the opening goal and created the second in a 2–1 league win for Feyenoord. On 17 April 2011, Miyaichi scored two goals and contributed two assists in Feyenoord’s 6–1 victory over Willem II, leading a revival after Feyenoord had conceded an early goal.

On 9 August 2011, Miyaichi was granted a work permit to play for Arsenal on the grounds of being an “exceptional talent” in view of evidence supplied by Wenger and the Japan Football Association, and was deemed free to represent Arsenal during the 2011–12 season. He was also included in Arsenal’s 23-man Champions League squad for the fixture against Udinese. On 23 August 2011, Miyaichi featured in the Arsenal Reserves against Wigan Athletic Reserves and scored in the 83rd minute.

On 20 September 2011, Miyaichi made his first team debut against League Two side Shrewsbury Town in the League Cup third round as a 71st-minute substitute. He also came on again in the League Cup as a substitute as Arsenal went on to win the match 2–1 against Bolton Wanderers.

During the reserve match against Fulham, on 7 November 2011, Miyaichi lasted 34 minutes before being forced off with an ankle injury, which would cause him to be out for weeks. Despite being in the first team, Miyaichi admitted he still has a lot to learn.

On 31 January 2012, Miyaichi joined Bolton Wanderers on loan until the end of the season. Shortly after arriving at Bolton, manager Owen Coyle spoke of his admiration for the young player, even though Miyaichi had yet to play in a competitive match for the team. He played a behind-closed-doors game on 7 February against Preston North End where he scored the only goal in a 1–0 win and made his full debut when coming on as a half-time substitute for Martin Petrov in Bolton’s 2–1 home defeat by Wigan Athletic on 11 February. He made his first start, and scored his first goal, the following weekend in Bolton’s 2–0 FA Cup win at Millwall. He played 78 minutes of the game before being substituted. He made his first Premier League start the following weekend in Bolton’s 3–0 loss at Chelsea. He was voted February Player of the Month by the Bolton fans after his debut.

On 13 August 2012, Arsenal confirmed that Miyaichi had joined Wigan Athletic on a season-long loan. On 28 August 2012, he made his debut as a substitute in a 4–1 League Cup victory over Nottingham Forest. During his first game for the club he was able to provide an assist for Callum McManaman. He went on to make his league debut on 1 September in a 2–2 draw with Stoke City. On 9 March, he made his return as a substitute for Callum McManaman in a 3–0 FA Cup quarter final win away to Everton. Miyaichi picked up injury during the game which saw him sidelined for the rest of the season. He thus missed the rest of Wigan’s historic cup run where they went on to lift the 2013 FA Cup.

Miyaichi received his first call up to the senior team for the 2014 World Cup qualification against Uzbekistan in February 2012, though he didn’t feature in the game.

Miyaichi made his debut on 23 May 2012 in a friendly against Azerbaijan where he came on as a 60th-minute substitute in a game that ended 2–0 to Japan. He made his second appearance against Brazil to again play as a substitute in a 4–0 Japan loss.

Miyachi made an early return to the Emirates from his loan move at Wigan due to injury. He went on to make his UEFA Champions League debut on 28 August 2013 in a 2–0 win over Fenerbahçe.

On 18 June 2015, the Hamburger Morgenpost announced that Miyaichi had signed a three-year contract with FC St. Pauli in the 2. Bundesliga, describing the winger as a player with “huge potential”. Miyaichi’s transfer was confirmed on the club’s website the next day, where it was revealed that he will wear the number 13 shirt for the upcoming season.