Brown appeared in his first game with the Windsor Spitfires on September 28, 2014, scoring a goal against Justin Nichols of the Guelph Storm in a 2–1 loss.

During the 2015–16 season, Brown set a career high with four points in a game, scoring a goal and earning three assists in a 5–3 win over the Flint Firebirds on January 21, 2016.

Brown would record another four point game later in the season, again scoring a goal and adding three assists in a 6–4 win over the Kitchener Rangers on March 17.

The Spitfires hosted the 2017 Memorial Cup, and Brown made his debut on May 19, being held off the score sheet in a 3–2 win over the Saint John Sea Dogs.

In his second game, Brown scored his first Memorial Cup goal against Carl Stankowski of the Seattle Thunderbirds, and added two assists, in a 7–1 victory.

After making the team out of training camp and beginning the 2017–18 season in the NHL with Ottawa, Brown returned to the Spitfires at the end of October.

In January 2018, Brown was traded to the Kitchener Rangers along with Austin McEneny in exchange for Grayson Ladd and a package of four draft picks.

The next day, on January 27, Brown scored his first two goals with the Rangers against Garrett Forrest on the Flint Firebirds, and added an assist in a 5–3 victory.

In game six, Brown scored his first two OHL playoff goals against Anthony Popovich of the Storm, and added an assist in a 5–2 series clinching win.

[15] On September 25, 2021, Brown was traded to the St. Louis Blues along with a conditional 4th round 2022 draft pick in exchange for Zach Sanford.

[21] As a free agent from the Blues, Brown was signed to a one-year, two-way contract with the Tampa Bay Lightning for the 2023–24 season on July 1, 2023.

[22] After missing the entirety of the season and having concluded his one-year contract, Brown continued his association with the Lightning by agreeing as a free agent to a professional tryout agreement (PTO) for Tampa's 2024 training camp.

[23] Following his PTO, on October 7, 2024, Brown signed a one-year contract with the Syracuse Crunch, Tampa Bay's AHL affiliate, for the 2024–25 season.