Massey came through the underage ranks at Bray Wanderers and made the breakthrough to the senior team in 2008. He made his professional debut in a League of Ireland Cup tie against Shamrock Rovers in May 2008 and went on to play five times that season for the club. In 2009, Massey made 34 appearances and scored his first senior goal against Shamrock Rovers, before going on to score three more goals that season. Massey played 31 times for Bray in the 2010 season and was also named the Supporters' ClubPlayer of the Month for April of that year. He appeared 26 times and scored one goal for Bray in 2011, and added another 27 league appearances in 2012.
Dundalk
Massey left Bray in December 2012 and, despite interest from Bohemians, he signed for Stephen Kenny at Dundalk. He cited Kenny's pledge to utilise him in an attacking full-back role, as opposed to the more defensive game he played at Bray, as being one of the deciding factors for the move. Massey made his debut for the club against Shamrock Rovers on the opening night of the 2013 season. He went on to score four times in 30 league appearances as Dundalk finished second in the league to champions St Patrick's Athletic. Massey stayed with Dundalk for the 2014 season and was part of a defence that kept sixteen clean sheets in the league. He also formed an effective partnership down the left-hand side with Daryl Horgan. In July 2014, Massey made his European debut in the Europa League against Jeunesse Esch. He was named the League of Ireland Premier Division Player of the Month for September 2014 after his brace of goals helped Dundalk to beat Shamrock Rovers in the LeagueCup final that month. Those two goals came a week after scoring a free kick in a 5−0 rout of Derry City in the league. He played in all 33 league games, scoring two further goals in wins over Sligo Rovers and UCD, as Dundalk won the Premier Division title. Massey then signed a new contract with the club to extend his stay until the end of 2015. In 2015, Massey went on to make 32 league appearances for the club, scoring four goals in the process, as Dundalk once more won the Premier Division title. In April 2015, his form led to calls in the media for his inclusion in the Republic of Ireland national team and manager Martin O'Neill indicated that he would be following Massey's performances closely. He also appeared in both Champions League Second Qualifying Round matches, as Dundalk were eliminated by BATE Borisov. In the first leg in the Borisov Arena, Massey was involved in an altercation with Vitali Rodionov after BATE's second goal, with video footage later revealing Massey had been headbutted. Despite this, UEFA imposed no sanction following a public apology from Rodionov. In November 2015, Massey appeared in the FAI Cup Final, in which Dundalk beat Cork City 1–0 after extra-time. He was named in the PFAI Premier Division Team of the Year at the end of the season. In 2016, Massey played every minute of all 6 of Dundalk's UEFA Champions League qualifier games as they became the first ever Irish side to reach the play-off round. This included providing an assist for David McMillan to score his second goal in a 3−0 victory over BATE Borisov in the Third Qualifying Round. Massey received significant exposure due to this achievement, appearing on RTÉ's Saturday Night with Miriam in August 2016.
Futsal
Massey also had a career in Futsal before focusing completely on association football. He credits the game with having a huge influence on his skills as a football player and improving his confidence on the ball. Massey made three appearances in the 2007–08 UEFA Futsal Cup for Shamrock Rovers, scoring two goals. His debut in this tournament took place in August 2007 when Rovers faced Politekhnik Yerevan. In 2008, Massey went on to represent the Republic of Ireland U21 Futsal team on 3 occasions, scoring 2 goals. He also made 5 appearances for the Republic of Ireland national team in the UEFA Futsal Championship qualifying rounds. His brother, Lloyd, also played Futsal for Shamrock Rovers and the Republic of Ireland national team. They played alongside each other for the national team at 3 UEFA Futsal tournaments.
Personal life
Massey worked as an electrician in the early part of his career to supplement his income alongside playing part-time football. In 2014, Massey balanced training and matchday commitments at Dundalk with working a few mornings a week as an electrician in the Jervis Shopping Centre in Dublin, however he gave this up at the beginning of 2015 to go full-time.>
Honours
Club
;Dundalk
League of Ireland Premier Division: 2014, 2015, 2016, 2018