The NHL's Department of Player Safety made the announcement on the league's official website.
With 2:33 to play in Edmonton's 3-1 loss, Hall crossed centre ice and stuck his leg out, levelling Clutterbuck and forcing him to leave the game.
NHL discipline czar Brendan Shanahan said it wasn't an accidental play.
"Although this play happens quickly, Hall is in control of himself, and in control of this hit," Shanahan said in a video explanation. "He makes the decision to step up and deliver a low check on a player who is not engaged with him whatsoever."
Shanahan added: "One of the contributing factors that elevate this kneeing penalty to a suspension is the fact that at no point does Clutterbuck control the puck, have possession of the puck, or have any reasonable expectation of contact in this situation."
Hall was assessed a major penalty and game misconduct on the play.
Shanahan also noted other factors that weighed into his decision, including Cluttberbuck suffering an injury and leaving the game, and the fact Hall has never been suspended in the NHL.
The 21-year-old Calgary, Alta. native will forfeit $9,729.72 US in annual salary based on the terms of the Collective Bargaining Agreement. The money goes to the Players' Emergency Assistance Fund.
Earlier this week, Vancouver Canucks forward Jannik Hansen was handed a one-game suspension for an elbow to the head of Chicago Blackhawks forward Marian Hossa.