The second-row will miss the opening two rounds of Heineken Champions Cup pool matches against Sale Sharks on 16 November and Exeter Chiefs on 23 November.
The decision has been made to manage the 25-year-old's workload in order to keep him as fresh and fit as possible throughout a busy 14-month period which started with the build-up to the World Cup, will carry on through the Six Nations and then on to Scotland's summer tour of South Africa and New Zealand next July.
However, Gray is getting a six week break due to the "cumulative" wear and tear on the second row in the last year.
"He did not play a lot of footie before the World Cup because of injury but he has played a lot for us and long term, from a Scottish perspective with the Six Nations and a pretty challenging summer tour, he is being managed for a little longer," said Rennie.
"He will have six weeks out and I anticipate him being back in time to face Leinster prior to Europe round three (on November 30)."
Another of the World Cup contingent, Ali Price, is recovering from his foot injury sustained in Japan and could come into the reckoning for the first European Champion's Cup game against Sale in a fortnight.