McKenzie played four seasons of NCAA Division I college hockey for the Miami RedHawks of the CCHA.

Following his senior year at Miami University, on April 12, 2013, the Dallas Stars of the National Hockey League (NHL) signed McKenzie to a two-year entry-level contract beginning with the 2013–14 AHL season, but he made his professional debut near the end of the 2012–13 season with their AHL affiliate, the Texas Stars, on an amateur tryout contract.

[1] In the early stages of the 2014–15 season, McKenzie made his NHL debut with the Dallas Stars on October 18, 2014, against the Philadelphia Flyers.

After five seasons within the Stars organization following the 2017–18 campaign, McKenzie left as a free agent and agreed to a two-year, one-way contract with the Vegas Golden Knights on July 1, 2018.

Leaving the Blues organization as a free agent, McKenzie opted to reunite with the Texas Stars of the AHL, securing a two-year contract on August 6, 2021.