The club said on their website (www.wasps.co.uk) that Haskell would not be considered for selection but hoped he would be back in contention for the game against Italy's Zebre the following weekend.
"James is fine within himself, but he took a significant bang to the head on Sunday and we don’t feel it right to push him to meet the tight deadline for a six-day turnaround," said director of rugby Dai Young.
"We would obviously all like for James to be involved in our big game against Toulouse, James included, but the most important thing is for him to feel completely right and under no pressure to make the game this weekend.
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"This is first time he has suffered concussion and we have told him to take extra time, with the aim of being fit for Zebre in the final pool round."
Haskell came off the bench and then appeared to lose consciousness after being spreadeagled in a tackle in the 22-16 victory over Leicester last Sunday.
The player, who had been out for nearly seven months due to toe surgery, was able to walk off after several minutes of treatment.
The scare was an added concern for England's head coach Eddie Jones, who is already grappling with several injury problems among his forwards ahead of the Six Nations starting next month.
(Reporting by Alan Baldwin, editing by Pritha Sarkar)
