Brodie Retallick will sit out the Chiefs' Super Rugby clash against the Hurricanes after the lock complained of suffering headaches.
Concern was shown over Retallick during their clash against the Waratahs on Saturday night after he copped a blow to the head.
Taken off the field for a concussion test, the 26-year-old passed but didn't return to the pitch.
"Brodie is one, he took a knock on the weekend and he's still got headaches yesterday so not enough time to pass the protocol so he's out for the weekend," Rennie said.
"He did pass the [head injury assessment] and we could have put him back on but we erred on the side of caution there. [We're] happy we did that, he said he's not feeling too bad but we're not going to risk that."
The injury could be a worry for Steve Hansen and co with Retallick joining a host of All Blacks who've battled concussion injuries in 2017 including Dane Coles who's yet to return to rugby, as well as Sonny Bill Williams, Ben Smith and Beauden Barrett.
Retallick has been replaced in the Chiefs side by Michael Allardyce.