Born in Glostrup, Schöne began playing youth football with Himmelev-Veddelev BK and moved on to Tåstrup B.70 and then Lyngby. In 2002, he moved to the youth team of Eredivisie club Heerenveen. He spent four years with the team without playing any league matches then moved to Eerste Divisie club De Graafschap in 2006. In his first season, he helped De Graafschap win promotion to the Eredivisie. In his two seasons with De Graafschap, he scored 12 goals in 70 matches.
N.E.C.
Schöne signed for NEC in summer 2008. He scored the winning goal for NEC away at Spartak Moscow in December 2008, which sent the team through to the next round of the UEFA Cup. The club and the fans picked him as NEC's player of the year, a title he also won at his previous club, De Graafschap.
Ajax
On 18 April 2012, Schöne joined Ajax on a contract valid until 2015. A number of other Danish players had played for Ajax, including Michael Laudrup, who had been a role model for him throughout his career. The club and the fans picked him as the player of the year in 2014. On 2 March 2015, he signed a new contract lasting until summer 2017, and on 22 February 2017, he signed a new contract lasting until summer 2019. On 27 February 2019, he became the international player with the most games played for Ajax, by surpassing Søren Lerby's 269 games. On 5 March 2019, in the UEFA Champions League, Schöne scored Ajax's final goal of the Round of 16-second leg against Real Madrid, by converting a direct free kick that went past the Real Madrid goalkeeper Thibaut Courtois. The victory completed a surprise comeback, the Dutch side winning 4–1 at the Santiago Bernabéu Stadium and 5–3 on aggregate to knock the European Champions out of the Champions League.
Genoa
On 9 August 2019, Schöne joined Italian Serie A club Genoa C.F.C. on a two-year contract. The reported fee was €1.5 million. He scored his first goal giving the lead in an eventual 2–1 loss against Milan. In the same match, he also missed a 90th minute penalty kick.
International career
Youth
Schöne began his international career with the Denmark national under-16 team, scoring a goal on his debut in August 2001. He played a total of ten matches and scored one goal for the under-17 and under-18 teams from July 2002 to March 2004. After joining De Graafschap, Schöne made his debut for the under-21 team in March 2007. He played a total nine matches and scored one goal for the under-21s until October 2008.
Senior
On 12 August 2009, on his debut for the Denmark senior team in a friendly against Chile, Schöne scored less than a minute after being put into action in the second half. The goal was the equaliser in an eventual 1–2 loss at the Brøndby Stadium. He was unable to play in the 2010 FIFA World Cup in South Africa because of a knee injury. In 2018 he was named in Denmark's squad for the 2018 FIFA World Cup in Russia. He played in three matches, starting in one, but did not score.
