The 30-year-old loose forward lasted just five minutes in the Brumbies' season opener against the Melbourne Rebels last week after being hit in the head while making a tackle.
Pocock failed a Head Injury Assessment and coach Dan McKellar said they would need to be careful about managing his return from his third concussion in less than 12 months.
The openside flanker, who has been replaced by Tom Cusack for the Chiefs' clash, would be missed but it was imperative he remained sidelined until completely cleared, according to team mate Scott Sio.
"I think it's good what World Rugby are doing around head knocks, we don't know the extent of the effects it can have," the prop told reporters earlier this week.
"I know 'Poey' would want to play and it looks to me he's not affected by any symptoms but we've just got to take the right measures there and make sure his health is the priority as well."
His health will also be closely monitored by Wallabies coach Michael Cheika ahead of the Rugby World Cup in Japan later this year and Australia's new selector has also urged to have a discussion about Pocock's playing position in the national team.
Former dual international Michael O'Connor was appointed on Wednesday to a new three-man selection panel, joining Cheika and incoming Director of Rugby Scott Johnson.
O'Connor, who was previously an independent selector with the Wallabies in 2006-07, said one of the key issues the panel would need to discuss was the best way to use Pocock for the Wallabies.
Cheika has preferred to use Pocock as a number eight with current captain Michael Hooper playing openside flanker, which has sacrificed a lineout option and big ball-runner amongst the loose forwards.
"You'd like to have a discussion about David Pocock playing number seven (openside flanker)," O'Connor told the Sydney Morning Herald.
"If (Cheika) has got strong reasons to keep things the way he has, well that's fine, but I think we should have the discussion and we will have the discussion.
"Hooper and Pocock are two of the best back-rowers in the game so were very fortunate. To leave one off, I think there is always going to be an argument.
"It's going to be interesting."
(Reporting by Greg Stutchbury in Wellington; Editing by Sudipto Ganguly)
