Holzer was selected by the Toronto Maple Leafs in the fourth round (No. 111) in the 2006 NHL Draft, but he remained in his native Germany for four years before heading to North America in 2010 to pursue his NHL dreams.

At 6-foot-3 and 215 pounds, Holzer is a strong, physical, steady defenseman who keeps it simple when it comes to moving the puck. He made his NHL debut with the Maple Leafs on Nov. 6, 2010, playing 12:46 of ice time during a 3-2 shootout loss to the Buffalo Sabres. Holzer played one more game for Toronto that season, three days later, but would not appear in another League game until 2012-13.

After two-plus seasons spent mostly in the American Hockey League, Holzer got his first NHL point Feb. 5, 2013, in his third appearance of the season, when he scored the game-winning goal for Toronto against the Washington Capitals. He played 34 NHL games in 2014-15 and, despite finishing 20th in ice time among Toronto skaters, ranked eighth on the Maple Leafs in hits and blocked shots with 117 and 53, respectively.

On March 2, 2015, Anaheim acquired Holzer in a trade for Eric Brewer and a fifth-round draft pick in 2016, but he did not play for the Ducks that season. He made his debut with Anaheim on Oct. 18, 2015, and played in 29 games, splitting time between the AHL and the NHL -- as he did for most of the next four seasons.

The Ducks traded Holzer to the Nashville Predators on Feb. 24, 2020.

Holzer has represented Germany internationally, including at the 2007 IIHF World Junior Championship, the 2010 and 2011 IIHF World Championships and the 2010 Vancouver Olympics.