Wines was charged by the AFL's match review officer for a high bump on Carlton's Cooper Lord in the second quarter of the Power's 54-point loss at Marvel Stadium on Saturday.
The bump on Lord, who had just kicked the ball, was considered high contact, severe impact and careless conduct, drawing a three-week suspension.
Lord was later substituted out of the game with concussion.
It rules Wines out of Friday night's match with finals-chasing Gold Coast at Adelaide Oval, when the Power will farewell Hinkley and the retiring Travis Boak.
Incoming coach Josh Carr will also be without the Brownlow Medal winner for the first two games of next season.
Gold Coast midfielder Alex Davies is also due to miss Friday's match, when the Suns can seal their first finals berth with a win, through a one-game ban for rough conduct on GWS's Ryan Angwin.
In the fourth quarter of the Suns' 35-point loss to GWS on Saturday, Davies appeared to be trying to lay a shepherd for a teammate, but gave away a free kick for his high contact on Angwin.
The incident was considered high contact, medium impact and careless conduct.
Several fines were handed out, with Adelaide star Izak Rankine slugged for staging and also careless contact with an umpire.Â
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