McKenzie's absence will follow the Power's 33-point win over Gold Coast on Saturday night, with the veteran backman subbed out of the contest at quarter time after injuring his ankle in a marking contest.
The 31-year-old was seen on crutches throughout the remainder of the night and will soon undergo scans to determine the full extent of the injury.
"He went off and had some X-rays," Hinkley said.
"We're optimistic he's not got a significantly damaged ankle, but he's got a badly sprained ankle so he'll miss some time."
McKenzie's injury could open the door to a recall for skipper Tom Jonas, who hasn't played at AFL level since Round 10, instead held to the SANFL given the form of Hinkley's rearguard across the past two months.
With a void now needing to be filled in his defensive third, Hinkley said Jonas will be first in line come selection for Round 18.
"Tom would have first dibs," the Port Adelaide coach said.
"He's always led the right way, he's been the right person to lead the club and if Trent does miss a bit of time, To is pretty clear in front at the moment for his turn to take that spot back."
Rioli, who booted two goals from 10 possessions in his return from illness and personal matters on Saturday night, won't partake in next weekend's trip to Melbourne to face the Blues as he plans to return home to Darwin for the anniversary of his father's passing.
A special service will be held this coming week, with Rioli to resume training in Adelaide following the ceremony.
Hinkley said the former Eagle had the club's full support amid an emotional time for the Rioli family.
"Junior has got a really special moment for his family," Hinkley said.
"It's his father's anniversary and he needs to be back in Darwin. He's got the full support of us as a football club.
"I think everyone can appreciate that it means an awful lot to him and his family and it's important for him to be there.
"We'll miss him next week but it was nice to have him back out there playing footy tonight and you could see he was having some fun."
Port Adelaide will travel to Marvel Stadium to face Carlton next Saturday at 4:35pm (AEST) with plans to notch up a 14th-straight victory.