Daw was born in Khartoum, Sudan, the third of his parents’ eventual seven children. His family fled the Second Sudanese Civil War, living in Egypt for three years, then moved to Australia in 2003. Majak attended school at MacKillop College in Werribee.

Daw was picked up with the ninth pick in the 2010 rookie draft. His draft pick gained international media attention. His career at North Melbourne began with playing for VFL club Werribee, where he continued to develop his game. He made his first appearance for North Melbourne in a pre-season NAB cup match against the Western Bulldogs on 20 February 2011. In April 2011, playing for Werribee, Daw kicked an impressive running goal from beyond 50 m out, prompting calls for his inclusion to the senior team.

On 4 June 2011, Majak Daw was racially abused by a Port Melbourne Football Club supporter while he was playing for the Werribee Tigers in the VFL. Daw stated that it “made [him] feel really small”. The man has since been banned from all VFL games until he completes an anti-racism workshop and formally apologises to Daw for the slur. The incident has led to renewed calls to stamp out racism in sport, with former Victorian Premier Ted Baillieu calling Daw a hero.

Daw was suspended from North Melbourne in February 2012 and remanded to the Werribee Tigers for an indefinite period for lying to the club and coach Brad Scott about a “night on the town” during a period in which he was recovering from knee surgery.

In 2013, Daw had an excellent showing in the 2013 NAB Cup, which prompted calls for his inclusion in the Senior Side. When tall forward Robbie Tarrant went down with a thigh injury, Daw was brought in to replace him and make his debut in Round 4 against the Brisbane Lions. In the first minute of the game, Daw marked the ball inside 50, and kicked his first AFL goal with his first AFL kick. However, his debut ended on a sour note when he collided with teammate Ben Cunnington and suffered a concussion before quarter time, and he took no further part in the game. North went on to win the game by 63 points.

On 1 July 2014, Daw was charged with three counts of rape relating to an alleged sexual assault incident in Altona North in 2007. He had been previously arrested and interviewed over the allegations in May 2014. Daw denied the allegations, while North Melbourne stated that he would remain available for selection. On 3 December 2015, Daw was found not guilty on all counts.

He was delisted in October 2015, however, he was re-drafted in the 2016 rookie draft.

In 2016, Majak Daw won mark of the year after taking a specky against Collingwood. Majak played the most games in a season in his career at that point with nine in addition to playing in his first final, which was in the elimination final against Adelaide and kicking four goals despite North Melbourne losing 141–79.

In 2017, after having a season full of injuries and only managing to play seven games in total, at the end of the 2017 AFL season Daw eyed more versatility as an AFL player.

In the 2018 offseason, Daw changed his position from a forward to a defender. Daw sought this change as he thought it was his last chance at thriving in the AFL. Majak played his first game as a defender against Carlton in the AFLX series. Later on in round 3 against Melbourne, Daw officially played his first game as a defender. Since debuting in his first game as a defender Daw has led North Melbourne to the number-2 defense in the AFL.

On 18 December 2018 Daw abandoned his vehicle on the Bolte Bridge and jumped into the Yarra River 25 metres (82 ft) below. Motorists on the bridge raised the alarm around 11 pm and he was recovered from the river by police and paramedics. He suffered broken hips and pelvis. In July 2019, Daw made a return for the North Melbourne VFL affiliate against Sandringham, the VFL affiliate of St Kilda. Daw made his AFL return on 1 August 2020 in a win against Adelaide, kicking one goal.