He made his professional debut in 2013, and won the SuperLiga title in his final season with Red Star before completing a £5.1 million move to Liverpool.

[7] Throughout autumn, Grujić was scouted by a number of high-profile European teams, including Liverpool, Internazionale, Juventus, Chelsea, and Milan.

On 20 August 2016, Grujić made his Premier League debut for Liverpool in a 2–0 loss against Burnley, coming on in the place of Adam Lallana in the 78th minute.

[14] Grujić's first goal for Cardiff came in a 2–1 home victory over Barnsley on 6 March 2018, scoring from range just after the start of the second half.

[20] On 25 September 2020, Grujić started in the EFL Cup tie against Lincoln winning 7–2 and scored a goal.

[24] In May 2016, Grujić made his full international debut for the Serbia national team after coming on in place of Nemanja Matić in a 2–1 win against Cyprus.

[25] In June 2018, he was selected in Serbia's squad for the 2018 World Cup,[26] but he failed to make any appearances in the competition.