After graduating from high school, Heinen earned a scholarship to play for the Denver Pioneers men's ice hockey team.

On February 24, 2020, while in his fourth season with the Bruins, Heinen was dealt to the Anaheim Ducks in exchange for Nick Ritchie.

[1] While with the Sockeyes in the 2012–13 season, he recorded 63 points[1] as he led the team to the Pacific Junior Hockey League championship title.

[5] In his only BCHL season, Heinen led the Eagles in scoring with 62 points in 57 games and won the junior A league's Rookie of the Year Award.

[6] After graduating from Langley Christian High School in 2013, Heinen earned a scholarship to attend and play for the University of Denver.

[12] As a result, he was named the inaugural recipient of the ASN Player of the Year Award[13] and earned First-Team All-NCHC Honors.

[15] Prior to the 2016–17 season, Heinen participated in the Bruins training camp[17] before being named to their opening night roster and making his NHL debut against the Columbus Blue Jackets.

[26] By December, Heinen was playing alongside Riley Nash and David Backes on a third line head coach Bruce Cassidy described as having a "200-foot game".

[28] Upon beating the Maple Leafs, Heinen started on the Bruins' first line against Steven Stamkos of the Tampa Bay Lightning during Game 1.

Although he remained at the NHL level, Heinen was pulled in and out of the lineup and experienced two separate 11 game pointless streaks.

[37] During the post-season, he played on the third line along with Charlie Coyle and Marcus Johansson,[38] and recorded two goals and six assists in 24 games as the Bruins reached the Stanley Cup Finals.

[37] On February 24, 2020, while in his fourth season with the Bruins, Heinen was dealt at the NHL trade deadline to the Anaheim Ducks in exchange for left winger Nick Ritchie.

[39] Heinen scored his first goal with the team on February 29, against the Pittsburgh Penguins,[40] but was ultimately unable to match his previous offensive efforts in the following season.

By April 2022, 14 of his goals had come at even strength, ranking him fourth on the team behind Guentzel, Sidney Crosby, and Bryan Rust.

[49] After playing in the preseason with the Bruins, Heinen went unsigned to start the season due to salary cap issues, but he officially returned to Boston on October 30, 2023, signing a one-year, $775,000 contract with the team.