Berube joins the Tampa Bay Lightning's Jon Cooper and the New York Islanders' Barry Trotz as finalists.
The Jack Adams is presented annually to the head coach who has "contributed the most to his team's success."
"I am proud of Craig for being a finalist for the Jack Adams," said Blues President of Hockey Operations and General Manager Doug Armstrong. "He and his staff have developed a strong relationship with our players and established a clear sense of direction for our team."
Berube took over as Head Coach of the Blues on Nov. 19, 2018. From then on, he led the club to a 38-19-6 record and a third-place finish in the Central Division. From Jan. 1 to the end of the regular season, the Blues went 30-10-5, accumulating the most points among all teams in that span.
Berube guided the Blues to become just the seventh team since 1967-68 to earn a postseason berth after being last in the NHL standings at any point after New Year's Day. Berube coached the Blues through a franchise-record 11-game win streak from Jan. 23 to Feb. 19 and a 12-1-1 mark in February, which tied a franchise mark for wins in a calendar month.
Berube, a first-time Jack Adams finalist, could become the fifth coach in Blues history to take home the trophy (Ken Hitchcock, Joel Quenneville, Brian Sutter, Red Berenson).
Members of the NHL Broadcasters' Association submitted ballots for the Jack Adams Award at the conclusion of the regular season, with the top three vote-getters designated as finalists. The award winner will be announced Wednesday, June 19, during the 2019 NHL Awards in Vegas.
Blues forward Ryan O'Reilly has also been named a finalist for the Selke Trophy and the Lady Byng Trophy.
