McGlinchey played youth football with Scottish club Celtic, where he made his professional debut. After spending time on loan to Dunfermline Athletic, he joined Central Coast Mariners in the A-League, where he made over 100 appearances. In his time at the club he spent periods on loan at Motherwell in 2010 and with Vegalta Sendai in 2014. He joined Wellington Phoenix in 2014 after securing a release from the Mariners.
McGlinchey represented Scotland at under-20 and under-21 level, but changed allegiance to New Zealand, his country of birth, at senior level. He was a member of the New Zealand national team squad at the 2010 World Cup and was one of New Zealand's over-age players at the 2012 Summer Olympics. He has made over twenty-five appearances for New Zealand, scoring four goals.
McGlinchey, a midfielder, was brought through the ranks at Scottish giants Celtic and was persuaded by then-manager Martin O'Neill at the age of 17 to resist the temptation to sign a professional contract with Manchester United and sign with the club he supported as a youngster. McGlinchey made his Celtic debut against Livingston as a substitute in December 2005. It was his sole appearance for the Scottish Premier League team, as O'Neill was replaced by Gordon Strachan and McGlinchey found himself moving to the fringes.
During the 2007–08 season he was then loaned out to Scottish First Division club Dunfermline Athletic until 20 January 2008. Although McGlinchey was successful during his loan deal at the First Division club, his loan was terminated early after he suffered a groin injury. He was released by Celtic in May 2009.
McGlinchey then had a successful trial with Central Coast Mariners in the A-League, signing a two-year deal with the club.
He made his Mariners debut against Melbourne Victory in the A-League season opener on 6 August 2009, and also scored his first goal for the club on debut in the 2–0 upset win over the reigning champions. It was also his first professional goal ever.
With the 2009–10 A-League season drawing to a close, McGlinchey decided to seek more first team football in the off season as buildup to the 2010 FIFA World Cup, signing a season-long loan deal with Scottish Premier League club Motherwell.
McGlinchey tried to leave the Central Coast Mariners on a free transfer but in August 2014, it was ruled that the player was still contracted to the Mariners. The PFA argued unsuccessfully that McGlinchey should be able to move to Wellington Phoenix on a free transfer as the club had been sold to new owners. However, on 11 September 2014, Central Coast Mariners conceded they would no longer pursue McGlinchey's services for the upcoming A-League season, citing his personal desire to no longer be involved with the club as a major contributing factor, and that following the receipt of compensation from McGlinchey his contract was terminated.
McGlinchey signed a loan contract with the Scottish side in February 2010 for the remainder of the 2009–10 season, and made 8 appearances.
On 23 December 2013, Central Coast Mariners announced McGlinchey would be going on a year loan spell to Vegalta Sendai, following Graham Arnold who had been recently appointed head coach. On 11 June 2014 Vegalta Sendai announced that they had terminated McGlinchey's loan.
On 12 September 2014, McGlinchey signed a two-year contract with Wellington Phoenix after securing his release from Mariners the day before.
McGlinchey was eligible to play for Scotland, the Republic of Ireland and New Zealand. His father, Norrie McGlinchey was a footballer playing in New Zealand, he represented Stop Out and Hutt Valley United during his career. The McGlinchey family returned to Scotland when Michael was one year old.
McGlinchey played two games for Scotland at the 2007 FIFA U-20 World Cup against Costa Rica and Nigeria.
In 2009, he took advantage of a FIFA Congress resolution which removed the age limit for changing associations for players who had already played for a country's national team at age group level and declared himself available for selection for the New Zealand All Whites. He was then included by New Zealand manager Ricki Herbert in the squad to face Jordan, before the 2010 World Cup play-off matches against Bahrain. McGlinchey made his New Zealand debut on 9 September 2009, in the match against Jordan.
McGlinchey played a pivotal role in the Inter-confederation play-off match against Bahrain in both the away leg in Ar Rifa` off the bench as a second-half substitute and made the starting XI in the home fixture in Wellington which New Zealand went on to win 1–0 thanks to a first half goal from striker Rory Fallon.
On 10 May 2010, McGlinchey was named in New Zealand's final 23-man squad to compete at the 2010 FIFA World Cup. He was one of New Zealand's three over-age players at the 2012 Summer Olympics, playing in all three of their matches in group C.As of 17 April 2017
As of match played 1 September 2017. New Zealand score listed first, score column indicates score after each McGlinchey goal.
Central Coast Mariners:A-League Premiership: 2011–12
A-League Championship: 2012–13
OFC Nations Cup: 2016
PFA A-League Team of the Season: 2012–13