Brahim began his career at his hometown club Málaga, before moving to Manchester City in 2015 as a 16-year-old for an initial £200,000 fee. On 21 September 2016, Díaz made his first-team debut for City, coming on as an 80th-minute substitute to replace Kelechi Iheanacho in an EFL Cup tie against Swansea City. Five days later, he signed his first professional contract with City, for three years.

Brahim was born in Spain to Spanish parents from Melilla, but is eligible to play for Morocco due to the origin of his father. Brahim is a youth international for Spain, and made his first appearances at age 16, where he received praise for his performances for Spain’s U17s in the 2016 UEFA European Under-17 Championship.

On 21 November 2017, Brahim made his Champions League debut against Feyenoord, coming on in injury time for Raheem Sterling. On 19 December 2017, Brahim made his first club start, playing for 88 minutes against Leicester City in the League Cup. He made his Premier League debut on 20 January 2018, in a 3–1 victory over Newcastle United. and on 13 May, he received a winner’s medal after appearing sporadically in four more league games over the season.

On 5 August 2018, Brahim played the final 15 minutes in place of Phil Foden a 2–0 win over Chelsea in the 2018 FA Community Shield. Later that season, Brahim would score his first career goal for City, netting both times in a 2–0 win over Fulham on 1 November.

Following intense transfer speculation, coupled with his contract with Manchester City due to expire in June 2019, Brahim joined Real Madrid on 6 January, for a transfer fee of £15.5 million (€17 million). His contract, which runs until 2025, also includes potential add-ons, which could see the value of the transfer to rise to £22 million (€24 million). The transfer also includes clauses which stipulates a 15 per cent sell-on fee to be received by City, which would rise to 40 per cent should Brahim depart Madrid and transfer to “another Manchester club”.

He made his debut on 9 January 2019, coming on as a substitute in a 3–0 victory over CD Leganés in the Copa del Rey. His league debut came four days later, when he again came in as a substitute in a 2–1 win over Real Betis. He scored his first goal on 12 May 2019, in a 1–3 defeat at Real Sociedad.

On 4 September 2020, Real Madrid announced that Brahim would be loaned out to A.C. Milan for the duration of the 2020–21 season.