Tortorella went to Calgary's locker room at intermission following the first period Saturday night, which began with several fights and four game misconducts per team. Vancouver won the game 3-2 in a shootout.
"Mr. Tortorella's actions in attempting to enter the Calgary Flames locker room after the first period were both dangerous and an embarrassment to the league," NHL senior executive vice president of hockey operations Colin Campbell said in a statement.
"Coaches in the NHL bear the responsibility of providing leadership, even when emotions run high, and Mr. Tortorella failed in his responsibility to the game."
Tortorella's suspension runs through Feb. 2. He will miss six games starting with Tuesday night at Edmonton.