The star prop went to the sin bin for making shoulder contact with Sarah Togatuki's head early in Thursday's surprise 12-10 loss to lowly Wests Tigers.
She has received a one-game suspension for her grade-two careless high tackle and would risk missing an extra game by challenging the charge.
Undefeated through six rounds, the Sharks look likely to scrape into the top four despite finishing the regular season on a three-game losing streak.Â
The only way Cronulla can be ousted is if Parramatta pull off the upset of the season and beat premiership favourites the Sydney Roosters by at least 35 points.
Even if the Eels are able to record the biggest win of their NRLW history, the Sharks will still make finals if North Queensland beat Newcastle on Saturday.
But Wheeler is now unlikely to play in a mooted grand-final qualifier for the Sharks, who are hopeful Rhiannon Byers will shake off a knee injury by next week.
Second-rower Byers left the loss to the Tigers during the second half but has told club staff she is confident of being fit in time for finals.
Lock forward Brooke Anderson went for a head injury assessment late in Thursday night's game but will need to consult with medical staff on Saturday before being cleared to play next week.
Elsewhere, Roosters captain Isabelle Kelly remains hopeful injured State of Origin stars Tarryn Aiken and Jess Sergis will return in time for the finals.
Five-eighth Aiken could return from her shoulder injury to face the Eels on Sunday after being named in John Strange's extended squad on Tuesday.
"She's going to keep working day in day out with everyone and making sure she's doing what she can to be there," Kelly told AAP.
"But at the end of the day it's her well-being that we've got to look after."
But Kelly's fellow centre Sergis is still at least a week away from returning from a knee issue after also missing the back-end of last season through injury.
"She's putting herself in the picture to be there for future games like a few of the girls, but at the end of the day if they're not, they're not," Kelly said.
Kelly expects to face the Eels despite a minor ankle injury forcing her from the field late in last week's defeat of the Cowboys.
"It was a bit sore throughout the week but it's pulled up pretty good, nothing too serious which is positive," she said.
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