Brown, 23, was acquired from the Blues via trade from the Ottawa Senators on Sept. 25, 2021.
A St. Louis native, Brown has appeared in 17 games with the Blues this season, posting six points (three goals, three assists) and four penalty minutes.
Originally drafted 11th overall by Ottawa in 2016, the 6-foot-6, 218-pound forward has accumulated 15 points (four goals, 11 assists) and 10 penalty minutes in 47 career regular-season games.