In 2008, Son joined Hamburger SV's youth academy, scoring a goal in six matches during the 2009–10 season for Hamburger SV II. His 2010-11 season was impressive and he signed his first professional contract on his 18th birthday.
During the 2011–12 pre-season, Son scored 18 times in 9 matches. Over the course of the 2011–12 season, Son made 30 appearances for Hamburg and scored five goals, including crucial goals that helped Hamburg remain in the Bundesliga.
The 2012–13 off-season saw Son in a starting role for the team. Son finished the 2012–13 season with 12 goals in 34 matches in all competitions.
Son' transferred to Bayer Leverkusen in June 2013 on a five-year deal for a reported EUR10m. He scored three goals in his first three appearances for the team. He finished the 2013–14 season with 12 goals in 43 matches. He finished the 2014–15 season with 17 goals in 42 matches. Son started the 2015–16 season with Bayer Leverkusen, making two appearances.
On 28 August 2015, Son joined Tottenham Hotspur on a five-year contract, for GBP22m (EUR30m). Before the 2016-17 season, Son reportedly asked to leave Tottenham in an attempt to get more playing time, but stayed and ended the season with a total of 21 goals in all competitions.
Awards Son wins EA SPORTS Player of the Month
Son was named in South Korea's squad for the 2011 AFC Asian Cup, and at the tournament finals, scored his first international goal during a 4– 1 group stage defeat of India. He also played in the 2011 World Cup qualifier against the United Arab Emirates.
He played for the national team in the autumn of 2012 for two 2014 FIFA World Cup qualifiers, and was a regular call-up in friendlies and World Cup qualifying matches in 2013.
Son was named in South Korea's squad for the 2014 World Cup. Bayer Leverkusen refused the Korean Football Association request to allow Son to play in the 2014 Asian Games.
Son was selected for South Korea for the 2015 AFC Asian Cup in Australia, helping his to the final against the hosts, where he equalised in added time, but his team lost 2–1 after extra time.
Son scored a hat-trick in the second round of qualification for the 2018 World Cup. In June 2016, Son was named in South Korea's squad for the 2016 Summer Olympics, helping his team to top the group. South Korea was eliminated in the quarter-finals.