Henrique was born in Brantford, Ontario, to Joe and Teresa Henrique, the second-oldest of four brothers. His father is Portuguese and his mother is Polish. His paternal grandparents speak Portuguese; his father also speaks some Portuguese, while his mother speaks Polish. Joe Henrique farms 50 acres of tobacco and ginseng in Burford, Ontario, about 90 minutes southwest of Toronto.
On April 11, 2011, Henrique made his NHL debut for the Devils in a game against the Boston Bruins. He scored his first career NHL goal on November 3, 2011, against Sergei Bobrovsky of the Philadelphia Flyers. Two nights later, Henrique scored two breakaway goals against the Winnipeg Jets, the second goal being the game winner in overtime. With the absence of centre Travis Zajac due to injury, Henrique was matched up with wingers Zach Parise and Ilya Kovalchuk on the team's first line for a short time. Henrique recorded his first career NHL fight on January 10, 2012, against the Calgary Flames. The same night, he also secured his first Gordie Howe hat trick. He fought Flames' captain Jarome Iginla in the first period and went on to record an assist and score a shorthanded goal in the second period. Iginla also recorded a Gordie Howe hat-trick in the game, with a goal and two assists in addition to his fight against Henrique. Henrique was selected to compete in the NHL All-Star Rookie SuperSkills Competition in Ottawa on January 28, 2012. However, he did not participate due to a groin injury he received in a game against the Edmonton Oilers on January 11. He missed two games due to the injury and returned in a game against the Buffalo Sabres; he "tweaked" his groin again that night, initially causing him to withdraw from the competition. Rookie teammate Adam Larsson also pulled out of the Game due to wrist soreness. Henrique was replaced by New York Rangers left winger Carl Hagelin, while Larsson with Montreal Canadiens defenceman Raphael Diaz. In the Eastern Conference Quarterfinals of the 2012 Stanley Cup playoffs, in Game 7 against the Florida Panthers, Henrique scored two goals, the latter being the double-overtime winner sending the Devils to the Conference Semifinals. In doing so, he became just the second rookie in League history to score an overtime-winning goal in a Game 7. On May 25, Henrique scored 1:03 into overtime to eliminate the New York Rangers and send the Devils to the 2012 Stanley Cup Finals. This made him the first rookie to score two series-clinching overtime goals in the same playoffs. At the end of the season, Henrique was one of the final three nominees for the Calder Memorial Trophy, awarded to the NHL's top rookie. The award, however, ultimately went to Gabriel Landeskog of the Colorado Avalanche. On August 26, 2013, Henrique, as a restricted free agent, signed a six-year, $24 million contract with New Jersey. During the 2015-16 season, Henrique scored a career-high 30 goals, almost doubling his previous season's total of 16. He also recorded a career-high 50 points, finishing second in team scoring only behind Kyle Palmieri. On October 29, 2016, Henrique scored his 100th career goal in a home game against the Tampa Bay Lightning.
Anaheim Ducks
During the 2017–18 season, on November 30, 2017, Henrique was traded by the Devils, alongside Joseph Blandisi and a 2018 third-round pick to the Anaheim Ducks in exchange for Sami Vatanen and a conditional draft pick in 2019 or 2020. When Henrique faced his former team for the first time on December 18, 2017, he was given a tribute video and a tremendous ovation from Devils fans. Despite a Devils 5-3 win, Henrique managed to net a superb goal by lifting the puck past Devils defender Sami Vatanen.
International play
Henrique first played at the International stage for Canada at the 2010 World Junior Championships, in Saskatchewan, Canada. He helped the hosts claim the silver medal, registering 1 goal in 6 games. On April 29, 2019, Henrique was named to the Team Canada roster to make his full international debut at the 2019 IIHF World Championship held in Slovakia. Henrique helped Canada progress through to the playoff rounds before losing the final to Finland to finish with the Silver Medal on May 26, 2019. He finished the tournament posting 2 assists in 10 appearances.