Plekanec had four goals and an assist last week as the Canadiens started the season with three straight road wins.
He began the season with two goals, including the game-winner with 42.9 seconds remaining in regulation, in a 4-3 victory over the Toronto Maple Leafs on Wednesday.
Plekanec scored Montreal's lone regulation goal in a 2-1 shootout win over Washington on Thursday and closed the week with a goal and an assist in a 4-3 shootout victory over Philadelphia on Saturday.
Minnesota Wild goaltender Darcy Kuemper was named second star and Pittsburgh Penguins centre Sidney Crosby earned the league's third star.
Kuemper stopped all 46 shots he faced in helping the Wild become the fifth team since 1943-44 to begin a season with consecutive shutouts.
He recorded 16 saves in a 5-0 triumph over the Colorado Avalanche on Thursday and then completed the home-and-home sweep with 30 stops in a 3-0 win Saturday.
Crosby had three goals and three assists to lead Pittsburgh to a pair of season-opening wins. He had two goals and an assist in a win over Anaheim on Thursday, and followed with a goal and two assists in a 5-2 win in Toronto on Saturday.