The son of a tobacco and ginseng farmer, Henrique was selected by the New Jersey Devils in the third round (No. 82) of the 2008 NHL Draft. He joined the Devils at the start of the 2011-12 season after four seasons with Windsor of the Ontario Hockey League.

After finishing with 51 points (16 goals, 35 assists), most among NHL rookies behind Gabriel Landeskog and Ryan Nugent-Hopkins (52 each), Henrique had 13 points (five goals, eight assists) during New Jersey's run to the 2012 Stanley Cup Final. Two of the five goals came in overtime and were series-clinchers. He scored 3:47 into the second overtime of Game 7 in the opening round to eliminate the Florida Panthers, and his goal 1:03 into overtime of Game 6 in the Eastern Conference Final against the New York Rangers sent the Devils into the Stanley Cup Final.

The goal against Florida made him the second rookie in NHL history to score in overtime of a Game 7, joining Claude Lemieux of the 1986 Montreal Canadiens. The goal against the Rangers put Henrique into the NHL record books as the first rookie to score two series-clinching overtime goals in the same playoff season. He also had three game-winners, matching the record set by Montreal's Jacques Lemaire in 1968 and tied by Lemieux in 1986.

Henrique also led the Devils and was third in the NHL at plus-12 during the 2012 Stanley Cup Playoffs. He was one of three Devils to finish with a plus rating in each of the four playoff rounds.

After struggling during the 2012-13 season, Henrique bounced back by scoring 25 goals and 43 points in 2013-14. He became a 30-goal scorer for the first time in 2015-16.

Henrique and Taylor Hall were teammates in the OHL, helping Windsor to win back-to-back Memorial Cup championship titles in 2009 and 2010. They were reunited when the Devils acquired Hall from the Edmonton Oilers on June 29, 2016.

Henrique was acquired by the Ducks in a trade for defenseman Sami Vatanen on Nov. 30, 2017 and made his Ducks debut the next night. He scored his first NHL hat trick in a 5-1 win against the Devils on Dec. 17, 2023, and his 500th NHL point with an assist on Troy Terry's goal in a 5–3 win against the Nashville Predators on Jan. 9, 2024.

After seven seasons with the Ducks, Henrique was traded to the Edmonton Oilers with Sam Carrick in a three-team deal also involving the Tampa Bay Lightning on March 6, 2024. He signed a two-year, $6 million contract to stay with the Oilers on July 1, 2024, after he had seven points (four goals, three assists) in 17 playoff games for Edmonton, which reached the Stanley Cup Final and lost to the Florida Panthers in seven games.

Henrique had two shots on goal in 13:17 of ice time in his 1,000th NHL game, a 3-2 win overtime win for the Oilers against the Ottawa Senators at Canadian Tire Centre on Oct. 21, 2025. He was the first player to appear with Edmonton during the milestone.