Cripps was among four forced outs for the Blues' Round 19 meeting with West Coast as star forward Harry McKay (knee), midfielder Adam Cerra (hamstring) and defender Jordan Boyd (suspension) were also unable to play against the Eagles.
The Blues revealed at selection on Thursday that their skipper has been unable to train this week due to a knock suffered in last Saturday's win over Port Adelaide, with the extent of his setback potentially ruling him out of two total matches.
While Carlton will enter this weekend's matchup as clear favourites even without their leader in the middle, the Blues will be hoping Cripps is fit in time to face Collingwood at the MCG the following Friday in what shapes as a blockbuster affair for both clubs.
Cripps is listed as a test for that encounter and will be needing to prove his fitness in the days prior to the must-win matchup.
After Cerra was unable to be cleared for Round 19, the midfielder will sit out this weekend's action with an eye on making a return against the Magpies as he battles hamstring tightness, while both McKay and Boyd will be unable to feature in either match, with the latter rubbed out for three games due to a rough conduct dangerous tackle suspension.
McKay's home and away campaign is over due to a knee injury sustained against the Power, with the Coleman Medal winner likely leaning on a finals berth from the Blues to be a chance of playing again this year.
Carlton currently sit two points outside the top eight and could move into the finals frame this weekend if other results go their way. Next week's clash with Collingwood will see Michael Voss' side come up against the form team of the competition as spots for September become harder to come by, with Carlton likely needing four wins from their last six games to secure a top eight position by the cessation of August.
The Blues will be buoyed by the returns of rookies Lachie Cowan and Oliver Hollands this weekend, while Ed Curnow has also returned to Voss' side as midfielder Paddy Dow prepares for his first starting stint of the season after previously taking on the role as the team's tactical sub on multiple occasions.
Small forward Matt Owies remains up to two weeks away as he deals with a low-grade calf issue that forced him to miss the win over Port Adelaide, while Zac Fisher is looking to return from a hamstring injury and could do so this weekend through the VFL.
Ruckman Marc Pittonet remains on the sidelines as a week-to-week assessment as he continues to nurse a knee injury.