Hajrović started playing football at local clubs, FC Birr and FC Windisch, before joining Grasshopper’s youth academy in 2000. He made his professional debut against Luzern on 3 October 2009 at the age of 18. On 19 September 2010, he scored a brace, his first professional goals.

Hajrović’s younger brother Sead is also a professional footballer. They played together in Grasshopper, before Sead joined Arsenal in July 2009.

On 17 September 2011, he scored his first career hat-trick.

After representing Switzerland at youth levels, Hajrović made his senior international debut on 14 November 2012, in a friendly match against Tunisia. However, in June 2013, he decided that he would play for Bosnia and Herzegovina in the future.

In August 2013, his request to change sports citizenship from Swiss to Bosnian was approved by FIFA. Later that month, he received his first senior call-up, for 2014 FIFA World Cup qualifiers against Slovakia, home and away. He debuted in home loss on 6 September. Four days later, in the away game, Hajrović scored his first goal for Bosnia and Herzegovina, coming on from the bench in the 77th minute of the game. His very first contact with the ball after just a few seconds on the pitch resulted in a goal from long range, which brought Bosnia a crucial victory.

On 7 January 2014, Hajrović was transferred to Turkish club Galatasaray for a fee of €3.5 million. He made his competitive debut for the club against Bursaspor on 2 February. He scored his first goal for Galatasaray in a cup win over Tokatspor. Three weeks later, Hajrović debuted in UEFA Champions League against Chelsea. Hajrović won his first trophy with the club on 7 May, by beating Eskişehirspor in Turkish Cup final.

On 10 July 2014, Hajrović signed a four-year contract with German team Werder Bremen. On his competitive debut for the team, he opened the scoring against FV Illertissen in DFB-Pokal game. He made his league debut a week later against Hertha BSC. He scored his first league goal on 26 April 2015 against Paderborn 07.

In June 2014, Hajrović was named in Bosnia and Herzegovina’s squad for 2014 FIFA World Cup, country’s first major competition. He made his competition debut in the opening group match on 15 June, which ended in narrow loss to Argentina at the Maracanã Stadium.

Hajrović married his long-time girlfriend Lejla in May 2014.

On 31 August 2015, Hajrović was sent on a season-long loan to Spanish outfit Eibar.

Upon returning from loan spell, Hajrović managed to secure first-team spot at Werder Bremen. However, on 3 December 2016, he suffered a severe knee injury, which was diagnosed as anterior cruciate ligament tear and ruled him out for the remainder of season.

Hajrović returned to the pitch on 16 September 2017, over nine months after the injury.

On 31 January 2018, Hajrović joined Croatian side Dinamo Zagreb on a contract until June 2019. He made his official debut for the club in a comfortable away victory over Osijek on 10 February. On 4 April, he scored his first goal for Dinamo Zagreb in Croatian Cup tie against Rijeka. Hajrović won his first trophy with the club on 13 May, when they were crowned league champions. On 2 February 2019, Hajrović scored a brace against Rudeš, which were his first league goals for the team.

In July 2019, he extended his deal until June 2021.