The Queensland Reds fly-half was slapped with the ban for a high tackle on Waratahs pivot Berrick Barnes during last week's victory.
The Reds had considered appealing against the decision but Cooper has now ruled that out.
"I won't be appealing the 1 match suspension as I don't want to be a distraction to the teams prep," Tweeted Cooper.
Earlier on Wednesday, Queensland chairman Rod McCall said they would speak with SANZAR and may appeal.
"We are cognisant of the need to support our player if we feel he has been treated harshly and, in our opinion, we still strongly believe the tackle did not warrant suspension," said McCall.
"After taking the advice of legal representatives, the QRU first intends to discuss the matter further with SANZAR before making a decision whether to launch an appeal within the allowed 48-hour period."
But Cooper's tweet appears to have closed the door on the matter and Ben Lucas looks set to fill the void against the Sharks.
The Wallabies maverick will be available for the Super Rugby semi-finals if the Reds overcome their South African rivals.