Brodzinski attended Blaine High School where he was teammates with former Minnesota Wild center Nick Bjugstad.

After high school, Brodzinski played two seasons in the United States Hockey League (USHL) with the Fargo Force.

As a freshman he led all NCAA freshmen with 22 goals[1] and as a junior he was named to the National Collegiate Hockey Conference (NCHC) All-Conference First Team during the 2014–15 season.

[12] As a free agent from the Kings, Brodzinski signed a one-year, two-way contract with the San Jose Sharks on July 2, 2019.

[14] Assigned to AHL affiliate, the San Jose Barracuda, Brodzinski tallied 14 goals and 16 assists for 30 points in 44 games before the season was cancelled due to the COVID-19 pandemic.

On October 9, 2020, Brodzinski left the West Coast as a free agent in securing a one-year, two-way contract with the New York Rangers.