Born in Herten in the Ruhr region, he began playing club football with FC Schalke 04 in 1999. After several years with the club, he continued his training with Borussia Dortmund and SG Wattenscheid 09.
After spending a year in their youth setup, Demirbay was promoted to Borussia Dortmund II playing in third tier 3. Liga. On 21 July 2012, the first matchday of the 2012–13 season, he came to his debut in professional football in an away game against VfL Osnabrück, replacing Konstantin Fring from the bench. He scored in the 1–2 home defeat against 1. FC Saarbrücken.
In the 2013–14 winter break, he agreed to join Hamburger SV on a free transfer in July 2014. After injury issues and several caps for their second team in fourth tier Regionalliga, he made his Bundesliga debut in the 1–3 home defeat by VfL Wolfsburg on 19 April 2014.
Although performing well in 2014–15 pre-season games, he moved to 2. Bundesliga side 1. FC Kaiserslautern on a season long loan to in August 2014. There he became a first team regular, starting in 18 matches and being put in another four times.
Returning to Hamburg, he again played pre-season, before signing on a season long loan to Fortuna Dusseldorf on 25 August 2015.
Demirbay achieved international notoriety for making a sexist comment against female referee Bibiana Steinhaus, in violation of league rules. After being sent off by Steinhaus, he told her "women have no place in men's football". Demirbay telephoned Steinhaus after the match to apologize. As a sanction for his behaviour, he was given a five-game ban and was made to referee a junior league girls' football match.
Although not having a Turkish passport, Demirbay played international youth football for the Turkish Football Association. In March 2015, he was chosen by Germany U21 coach Horst Hrubesch, but was excluded from games due to injury. He was then selected for 2015 European Under-21 Championship in the Czech Republic, but did not play in any of the games.
Demirbay accepted a callup to the Turkey national football team on 17 May 2017, for a 2018 FIFA World Cup qualification against Kosovo, but rescinded the offer. Later in the same day, Demirbay accepted a callup to the Germany national football team for the friendly against Denmark on 6 June 2017, for the 2018 World Cup qualification match against San Marino on 10 June 2017 and for the 2017 Confederations Cup to be held from 17 June to 2 July 2017.
Demirbay made his international debut on 6 June against Denmark, where he was subbed on in the 77th minute for Leon Goretzka.As of 25 June 2017
(Germany score listed first, score column indicates score after each Demirbay goal)
FIFA Confederations Cup: 2017