The Oilers' defenseman was assessed a minor penalty for elbowing on the play.
"At the moment of impact, it's clear that the head is the principal point of contact and has been recklessly targeted," Shanahan said in a video on NHL.com that explains the suspension. "Landeskog is looking back for the pass and rotates his head, but the position of his head does not dramatically change."
Shanahan and the department of player safety examined Sutton's disciplinary history while making its decision.
"We've also taken into consideration that although Sutton has played a physical game over his 14 years, he's been fined and suspended for various illegal checks," Shanahan said.
Sutton sat out Sunday's 4-2 win over the St. Louis Blues while the NHL made its decision.
Sutton will forfeit more than $57,000 in salary.