Hinkley had complained of severe back pain throughout the day and tests revealed he was suffering from a virus that would prevent him from flying to Tasmania on Friday.
Senior assistant Alan Richardson will take the reins as head coach in his absence at Blundstone Arena this weekend.
Club chief executive Keith Thomas said Hinkley would be fine and that he could have coached if the Power had a home game this weekend, but that the club wouldn't take any risk with his health.
"Ken was admitted to hospital last night with chronic back pain and subsequent tests have revealed that he is suffering from a virus.
"After consultation with our club doctor Damian Newberry it has been advised that Ken should not fly this weekend while he overcomes the effects of the virus.
"We expect Ken to make a full and speedy recovery. In fact, if our game was played in Adelaide this week he more than likely would have coached."
Thomas said Hinkley and Richardson's coaching similarities would mean Richardson's takeover this weekend would be seamless.
"We’ve often said Ken and Alan are very similar in the way they think about the game and in terms of their philosophies," he said.
"He has vast coaching experience in his own right and has worked closely with Ken here at Port Adelaide on game style and structures since day one of pre-season.
"Alan has the complete respect and confidence of the playing group and coaching staff and we are confident that his transition as senior coach for this week will be seamless."
Harry Thring is a reporter for AFL Media. Follow him on Twitter: @AFL_Harry.
