Rees is currently part of the elite England squad, while Cipriani is in the England Saxons group.
Wasps rugby director Tony Hanks said: "This is not a decision that has been taken lightly by Tom or the club.
"However, the disappointment of the delay in a return to fitness is secondary to Tom's health, comfort and long-term career.
"All parties believe that this is the best option for Tom and he will, of course, have the full support of the club through this difficult and frustrating time.
"There is always disappointment when any player is injured but we have a great medical team who work tirelessly to bring our players back to health."
England prop Phil Vickery will captain Wasps in their Challenge Cup opener against Racing-Metro 92 at Adams Park, leading a team that includes full-back Lachlan Mitchell following his recovery from mild concussion sustained during last weekend's Guinness Premiership victory over Northampton.
And Wasps head coach Shaun Edwards believes European rugby's second-tier knockout competition is about to move up a gear.
Wasps are among the principal contenders, along with current Premiership leaders Saracens.
And, given only the five pool winners will progress - three Heineken Cup teams complete the quarter-final picture next April - Edwards expects intensity levels to rise.
"With three Heineken Cup teams coming in at the quarter-final stage, it will make it much more competitive," he said.
"It will certainly make the trophy much more difficult to win, no shadow of a doubt about that."