Landeskog, drafted second overall by Colorado in June, was looking back to accept a pass in the neutral zone when Sutton stepped up in anticipation of delivering a hit.
Shanahan said Sutton is not considered a repeat offender as defined by the collective bargaining agreement but that the NHL could not ignore his history.
"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," said Shanahan.
Sutton, who had already sat out Sunday's game against the St. Louis Blues, will be eligible to return for his team's November 11 game against the Detroit Red Wings.
"I have been informed of and understand the league's decision, however, I had no intention of delivering an illegal check," Sutton said in a statement. "For 14 years, I've always played the game with respect and integrity and I will continue to do so when I return."
(Reporting by Gene Cherry in Salvo, North Carolina; Editing by Frank Pingue)