The NHL announced the suspension on Monday night.
Wisniewski was suspended for the high hit on Clutterbuck at the conclusion of play in the preseason game on Sept. 23 in Minnesota.
"He targets Clutterbuck's head ... and (Clutterbuck) is defenseless," NHL senior vice president of safety, Brendan Shanahan said. Shanahan also singled out Wisniewski as a repeat offender.
Wisniewski is eligible to return to the Blue Jackets lineup against Detroit on Oct. 25.