[10] Zucker has multiple tattoos: on his back, "USA" (a nod to his playing for the national team); on his chest, "Game Time" (in memory of his best friend, Nick Scheafer, who died in 2010 at the age of 19 in a car accident); and on his left arm, written in Hebrew, "In pursuit of perfection" (in honor of his Jewish heritage).

[19] He scored his first NHL goal against Petr Mrázek on February 17, 2013, in a Wild win over the Detroit Red Wings.

[20] On May 5, 2013, Zucker scored at 2:15 of the extra period to give the Wild a 3–2 victory over the Chicago Blackhawks, to pull within 2–1 in the Western Conference quarterfinal series.

[24] The only other NHL players who have scored within the first 10 seconds of two different games are Montreal's Bobby Rousseau (once in 1962–63, and once in 1965–66) and Yvan Cournoyer (both in 1973–74).

[25] During the 2016–17 season, Zucker set new career highs once again by playing in 79 games while recording 22 goals and 25 assists for 47 points.

[26] On May 2, 2018, Zucker was named a finalist for the King Clancy Memorial Trophy, along with P. K. Subban, and the Sedin brothers.

Zucker scored his 100th NHL goal on October 13, 2018, in a home overtime loss against the Carolina Hurricanes.

[29] Zucker received the 2018–19 King Clancy Memorial Trophy as "the player who best exemplifies leadership qualities on and off the ice and has made a noteworthy humanitarian contribution in his community.

[30][32] He made his Penguins debut on February 11 in a 2–1 loss to the Tampa Bay Lightning, playing on a line with Sidney Crosby.

[33] He scored his first two goals in a Penguins uniform against Carey Price in a 4–1 win over the Montreal Canadiens on February 14.

[34] Zucker later made his Penguins playoff debut against the Canadiens on August 1 in Game 1 of their first round series.

[43][44] He scored his first goal with Arizona on October 19 on a pass from Matias Maccelli on the power play in a 6–2 victory over the St. Louis Blues.

[45] On January 2, 2024, Nick Cousins of the Florida Panthers laid a dangerous check on Zucker's teammate, Juuso Välimäki near the boards.

[51] He scored his first goal for Nashville on March 13, knocking in a rebound from a Colton Sissons shot in a 4–2 win over the Winnipeg Jets.

[54] On July 1, 2024, Zucker signed as a free agent to a one-year, $5 million contract with the Buffalo Sabres.

[58] Zucker married Minneapolis-based sports and entertainment journalist and television personality Carly Aplin in mid 2016.