Taken at #16 in the 1994 National AFL Draft, and debuting in 1995 with the Melbourne Demons, he has been an almost permanent fixture with the club throughout his career. He has remained remarkably consistent in this time, moving from half back to the midfield and in recent years has moved between half forward and half back. Yze led the league in kicks in 2001, 2002 and 2004, while coming third behind Scott Camporeale and Nathan Buckley in 2000.
In 2007, Yze found struggling with his form over the pre-season. After a disappointing performance against St Kilda in Round 1, his streak of 226 consecutive AFL appearances was put to an end, with Melbourne decided to drop him for the Round 2 game against Hawthorn. Yze was then selected for Melbourne's Round 4 match against Fremantle and picked up a career-high 38-possessions and kicked one goal, being named as one of the best on ground for the day. Despite seeing very little first-team action in 2008 – the last year of his contract at Melbourne, Yze has declared his intention to continue playing football, even if that means he enters the draft, or plays at VFL level. At 30, Yze feels he could play on for another two or three years.
Due to Melbourne Football Clubs youth policy introduced at the end of Season 2008, Adem was delisted after only six senior appearances for the year, in which he kicked five goals. However these six games allowed Yze to notch up 300 senior appearances, which resulted in him gaining Lifetime AFL Membership. Yze expressed his desire to play on at another AFL club in Season 2009 declaring he would apply for the preseason draft, yet he conceded he had "stuff all" chances of being picked up by another club. However Yze declared he would play on regardless in 2009, even if it was at a suburban club, such as East Burwood, where his brother Damian Yze plays. Yze played with the Box Hill Hawks, which is aligned with Hawthorn in 2009 and joined the Shepparton Swans a year later.
He is also noted for being one of very few Muslims to play Australian rules professionally, although he does not actively practise Islam. Fellow Muslim, Bachar Houli, has stated that he hopes to follow in Yze's footballing footsteps.