Heed was selected by the Anaheim Ducks in the fifth round (No. 132) in the 2010 NHL Draft after he had 10 points (one goal, nine assists) in 27 games for Sodertalje in the Swedish Hockey League. He played six more seasons in the SHL and won the Le Mat Trophy as league champions with Skelleftea in 2013-14, and reached the finals the following two seasons. Heed also won the 2015 Salming Trophy as best defenseman when he had 37 points (10 goals, 27 assists) in 50 games.

Following the 2015-16 season with Skelleftea, Heed signed an entry-level contract with the San Jose Sharks on May 24, 2016.

In 2016-17, Heed played with San Jose in the American Hockey League, getting 56 points (14 goals, 42 assists) in 55 games. He ranked first among AHL defensemen in points per game (1.02, min. 25 games played) and fourth in points and was selected to the AHL Second All-Star Team.

On Jan. 11, 2017, Heed made his NHL debut, getting one shot in 16:29 of ice time in a 3-2 loss to the Calgary Flames. The Sharks re-signed him to a two-year contract on June 17, 2017.

In 2017-18, Heed scored his first NHL goal in a 4-1 win against the New York Rangers on Oct. 23, 2017 and finished the season with 11 points (three goals, eight assists) in 29 games.