As a child growing up in Melbourne's Western suburbs, Leckie actually aspired to play Australian rules football, his family supporting Essendon, however at 11 years old a change to a school in Sunshine with a more multicultural student body inspired him to take up football and he "never looked back".
Leckie was a member of Victorian State League Division 1 outfit, Bulleen Lions until 2 September 2009, where Leckie was signed to Adelaide United for a two-year professional contract. He made his A-League debut on 18 September for Adelaide United coming on as a substitute in the 75th minute against Melbourne Victory.
Leckie scored the winning goal in his first AFC Champions League match on 24 February 2010, against the reigning champions Pohang Steelers at Hindmarsh Stadium. He followed this up by scoring his second goal in as many games against Shandong Luneng in Adelaide's 2–0 win on Match Day 2 of the Champions League. Leckie is considered to be one of Australia's best young players.
Leckie started the 2010–11 season with a bang, scoring twice in Adelaide's first five games, earning wide praise for his entertaining and robust style of play and winning the favour of the Australian U19 side for their competing in the 2010 AFC Under-19 championships. At the end of the A-League season he signed for German side Borussia Mönchengladbach. He scored his first goals for his new club with a double in a 5–2 friendly win against Aberdeen FC On 9 July 2011. In early 2013, he was loaned out to Frankfurt and has since scored 3 goals in only 2 appearances for the reserve team.
On the 3 June 2013, Mathew made his loan move to FSV Frankfurt permanent, signing a three-year contract that runs till 2016. Mathew stated the move was made to maximise his personal development and to build on the successes of his first season spent at FSV on loan where he made 28 appearances and scored 4 goals.
On 7 May 2014, he signed a three-year contract with FC Ingolstadt 04. While playing for Ingolstadt, the club was promoted to the Bundesliga at the end of the 2014–15 season.
On 22 May 2017, it was announced that Leckie had signed for Hertha BSC for the 2017–18 season. He began his spell positively, appearing in many pre-season matches and assisting 2 goals in his first competitive appearance for the club in the first round of the DFB Pokal against Hansa Rostock. During his Bundesliga debut with Berlin, he scored a brace in a 2–0 win over VfB Stuttgart.
In August 2009, Leckie was selected to represent Australia in the AFF U19 Youth Championship 2009, where he opened up the score-sheet in the 4–1 win over hosts, Vietnam, in the semi-finals. Mathew was called up to the Australian Under-19s for the 2010 AFC U-19 Championship.
Ex-Australian National Coach, Pim Verbeek, named Leckie in the 25 man Socceroos squad for the AFC Asian Cup 2011 Qualifier against Indonesia. Leckie didn't make an appearance in the game which Australia won 1–0 to book their place in the Asian Cup.
Ex-Australian national coach Holger Osieck included Leckie in the squad for the international friendly against the Republic of Korea on 14 November 2012. Leckie came on as a late substitution with only limited time on the ball.
Australian National Coach, Ange Postecoglou, included Leckie in the squad for the international friendly against Costa Rica on 19 November 2013.
Leckie had an outstanding World Cup campaign resulting in pundits estimating his worth at $10 million. He was quoted saying he does not regret his decision to sign for German second division club FC Ingolstadt, recognising that he may have had offers from larger clubs following his World Cup performances. "So whether I could have maybe had other offers now after this World Cup if I hadn't signed, I never would have known."
Leckie was named as part of Australia's 2015 AFC Asian Cup squad. He started Australia's first game of the tournament against Kuwait, hitting the crossbar in the second half, and then providing the assist for James Troisi to score Australia's fourth goal of the match and helping Australia to a 4–1 win.
On 3 September 2015, Leckie scored his second goal for Australia, and his first since 2013, opening the scoring against Bangladesh in a 2018 FIFA World Cup qualifier. On 5 September 2017, Leckie scored his 6th international goal for Australia against Thailand.As of match played 6 September 2017. Australia score listed first, score column indicates score after each Leckie goal.
As of 11 September 2017
With Australia:AFC Asian Cup: 2015
AFC U-19 Championship: 2010 (Runners-Up)
AFF U-19 Youth Championship: 2010
FC Ingolstadt2.Bundesliga: 2014–15
Personal Honours:Adelaide United Rising Star: 2009–10