Henry joined the Toronto FC Academy in November 2008, and captained the team through two seasons in the Canadian Soccer League in 2009 and 2010.

He appeared for Toronto FC in the 2010 Nutrilite Canadian Championship against the Vancouver Whitecaps and a 2010–11 CONCACAF Champions League Qualifying match against Motagua. He also made his MLS debut and played in another 2010–11 CONCACAF Champions League Match against Árabe Unido during the 2010 season. He also played in an international friendly against Bolton Wanderers. He signed with Toronto FC on August 26, 2010 becoming the first TFC Academy player to sign for the first team.

On June 15, 2011, in a 0–0 away draw against New England Revolution, Henry drew high praise from Taylor Twellman who was commentating on the game. After coming on for Richard Eckersley in the second half against Real Salt Lake on April 28, 2012, he scored his first goal for Toronto in the 77th minute in a 3–2 away defeat. On August 21, the club announced that it had re-signed him to a long-term deal. During the 2011–12 CONCACAF Champions League, he made four appearances during the 2011 season and an appearance during the 2012 season. He also made two appearances in the 2012–13 CONCACAF Champions League during the 2012 season.

He was selected for the Canada U23 roster to partake in the 2012 CONCACAF Men’s Olympic Qualifying Tournament. After sitting out the first game he started and scored the opening goal against the United States U23, the match ended in a 2–0 victory for Canada.

Henry earned his first cap for Canada’s senior team August 15, 2012 in a friendly against Trinidad and Tobago. He started the match before being subbed out at halftime for Pedro Pacheco, the game ended in a 2–0 victory. On December 10, 2012 he was awarded the 2012 Canadian U-20 Player of the Year, receiving 37.8% of the vote and just beating out Samuel Piette for the award.

Henry scored his second goal for Toronto outside the penalty box in a 2–0 home victory over rival Montreal Impact in the Canadian Championship on April 24, 2013. Prior to the 2014 season he spent some time training with Premier League side West Ham United. After scoring mid-week in the Canadian Championship against Montreal Impact he scored the 92nd minute game winner against Columbus Crew in a 3–2 home victory May 31, 2014.

On June 27, 2013 Henry was listed as a part of the confirmed 23-man squad for Colin Miller’s Canada squad for 2013 CONCACAF Gold Cup.

In October 2014, it was officially announced that Henry had been sold to 2014–15 UEFA Europa League and Cypriot First Division participants Apollon Limassol, for an undisclosed fee in April 2014 prior to the commencement of the 2014 MLS season. Representatives from Toronto FC confirmed that the deal has a sell on clause and that they intended to enter into talks with Henry and Apollon Limassol with the hope of keeping the player on loan again for the 2015 MLS season.

Having previously had two training stints with West Ham in the Premier League after the player was recommended to manager Sam Allardyce by Ryan Nelsen, Henry signed for the club on January 3, 2015 on a “long term” contract for an undisclosed fee. He made his West Ham debut on August 6, 2015 in a 2–1 away defeat to Romanian side FC Astra in the Europa League qualifying stages. His team was eliminated as a result of the defeat. This was his only appearance and he left the club in December 2017 when his contract was cancelled by mutual consent.

On March 4, Henry was loaned by West Ham to Blackburn Rovers in the Football League Championship, on a one-month loan. He made his debut on the same day against Sheffield Wednesday, a 2–1 win for Rovers, a performance described by Rovers’ manager, Gary Bowyer as “magnificent”. In his second match for Blackburn on March 11, he got an assist in a 94th-minute goal from Jordan Rhodes to give them a 1–0 victory over Bolton Wanderers. In his third game for Blackburn, a 3–1 away win against Charlton Athletic, he sustained a hamstring injury which manager Bowyer said would mean the end of the season for Henry. With his loan cut short, he returned to West Ham United. He returned to Blackburn on loan on November 24, 2015.

On August 31, 2016, Henry was loaned by West Ham to Danish Superliga club AC Horsens for half a season. On October 23 Henry started his first game in the starting line-up, against Randers FC. The game resulted in a clean sheet and 1–0 victory for Horsens and Henry. In Henry’s second start with Horsens, he suffered an ACL tear, which would end his season. He went back to West Ham in start of January 2017.

On December 22, 2017, Henry was signed by Vancouver Whitecaps FC. On April 25, 2018 Henry was loaned to United Soccer League club Ottawa Fury until the end of May. According to Vancouver Whitecaps FC head coach Carl Robinson, the goal of the loan was to help Henry reach full fitness by getting competitive match time. Henry made three appearances for Ottawa, all of which were clean sheets, but was forced to sit out the last two games of his loan, one due to bronchitis and one due to fatigue. On May 29, he was reported to have returned to Vancouver. Henry would make his Whitecaps debut in June 2018, shortly after returning from Ottawa Fury on loan.

He scored his first league goal for Vancouver against Minnesota United in Vancouver’s 2019 MLS season opener on March 2.

On November 20, 2019, Henry was transferred to South Korean K League side Suwon Samsung Bluewings for an undisclosed fee.

Henry was named to the squad for the 2019 CONCACAF Gold Cup on May 30, 2019.

Henry scored his first goal for Canada on September 7, 2019 against Cuba in a CONCACAF Nations League match.