Sutton was originally suspended indefinitely and offered an in-person hearing to determine the length of his ban.
NHL discipline czar Brendan Shanahan announced the eight-game suspension on Saturday.
During the third period of Wednesday's 5-3 loss, Sutton left his feet while hitting Ponikarovsky near the boards with the primary point of contact being the head.
"While we acknowledge that on many big body checks the hitter's feet may at times come off the ice to a certain degree," Shanahan said in an online video, "we felt the degree in which Sutton's skates come off the ice was excessive."
Sutton was suspended five games earlier this season for a similar hit on Colorado Avalanche forward Gabriel Landeskog.