A product of Partizani Tirana academy, Muzaka begun his career as a talented youth player, which prompted Paris Saint-Germain to sign him in 2000.

Muzaka played for eight years for The Red Bulls, notably winning the Albanian Cup title and also having a brief spell in Greece with Iraklis as a loanee in 2004.

In the following years, he also represented Dinamo Tirana, Flamurtari Vlorë (twice) and Skënderbeu Korçë (twice),[2][3][4] achieving a great success with the latter, winning three Albanian Superliga titles between 2011 and 2014.

In January 2015, Muzaka returned to Tirana,[5] but his second spell was marred by consistent injuries and off-field problems, including with club president Refik Halili.

[6] He left the club in controversial fashion in January 2017, accusing Halili of not paying him accordingly during his time there; Muzaka filled an appeal at the Conflict Resolution Room of AFA and won, but is yet to take is wages.

He established himself as a starter in the 2003–04 season under coach Sulejman Mema playing 33 matches and scoring 10 goals winning his first trophy of career, the 2003–04 Albanian Cup and finishing 4th in the league.

[16] He missed the opening two league matches due to injury, and returned in action in September, making his competitive debut against his former team Partizani in the Capital derby; he came as a second-half substitute in place of Sabjen Lilaj and assisted Andi Lila last-minute winner for a 2–1 win.

[23] Muzaka was named in Dinamo UEFA Champions League squad, and made his competitive debut on 14 July 2010 in the first leg of second qualifying round against FC Sheriff Tiraspol ended in a 3–1 away defeat.

[3] Despite being the target of many Superliga teams, including his former side Tirana, Muzaka choose Flamurtari and signed a contract worth a reported fee €75,000 per season.

[35] In December 2013, Muzaka was a nominee for the Albanian Footballer of the Year award,[36] which was subsequently won by Teuta Durrës' Daniel Xhafaj.

[5] On 7 January he was officially unveiled as a KF Tirana player to the media, holding a press conference alongside the club's president Refik Halili and newly appointed director Devi Muka.

[42] On 22 April 2015, during the 2014–15 Albanian Cup semi-final second leg match against Laçi, Muzaka snapped his knee's ligament after a collision with Olsi Teqja and was stretchered off the field in the 46th minute.

[51] On 17 April, during the league match at Bylis Ballsh, Muzaka suffered another injury, a shoulder fracture which forced him to end of the season with six weeks remaining.

[60] On 30 January 2017, Muzaka joined Skënderbeu Korçë on a free transfer for a third time, taking the vacant number 17 for the second part of 2016–17 season.

[61] Manager Ilir Daja, who worked with him during his time at Tirana, called Muzaka a "valuable player", adding that "he has experience and speed".

[62] After two games as an unused substitute, Muzaka made his return debut on 19 February against Luftëtari Gjirokastër, scoring in the first half in an eventual 3–0 home win.

[71] In the returning leg of second qualifying round against Kairat, Muzaka came off the bench and assisted Sebino Plaku's goal as the team progressed passed 3–1 on aggregate.

[74] In Europa League, Skënderbeu was placed in Group B,[75] and in the opening matchday away against Dynamo Kyiv, Muzaka scored his team's only goal after an individual effort in an eventual 1–3 defeat.

[80] He concluded the 2017–18 season by contributing with 32 league appearances and scored 6 goals, his highest tally in five years, as Skënderbeu winning the championship for the 8th in history.

[81] In cup, he played 5 matches, including the final as the team defeated Laçi to clinch their first ever trophy, thus completing the domestic double for the first time in history.

[88] On 5 October 2019, he was substituted by Otto John in a 2–0 home win over Luftëtari Gjirokastër after suffering a heavy injury in the second half;[89] following the examinations, it was reported that Muzaka had completely tear the cruciate ligament of right knee, which left him sidelined for at least 6 months.

[90][91] Muzaka was first approached to the national team in September 2002 for three 2003 UEFA European Under-19 Championship first qualifying round matches against Russia, France and Luxembourg.

It was a start to forget for Muzaka, despite playing in all three matches as starter, as Albania lost all of them with hammering results and finished last in Group 9.

[98] After appearing in numerous friendlies, Muzaka was called up by coach Josip Kuže for the first two UEFA Euro 2012 qualifying matches against Romania and Luxembourg in September 2010.

He made an immediate impact and in the 87th minute he managed to find a head onto Ansi Agolli's free kick which he guided past the Romanian goalkeeper, which levelled the tie at 1–1 and earned Albania a very important and well-deserved point.

[100][101] In his youth, Muzaka was noted for his speed, technique, ball control and dribbling skills, also earning comparisons to Cristiano Ronaldo.