The 31-year-old only recently moved to the Rec, signing a short-term deal following his release by the Dragons in May, but he looks unlikely to play for his new club any time soon after dislocating his shoulder.
The injury is set to keep the former Exeter, Ospreys and Cardiff Blues tight-head on the sidelines for up to six months.
However, Bath head coach Todd Blackadder says the Aviva Premiership side will not be cutting him loose, claiming they have a duty of care to see Mitchell through his rehab.
"We got Craig on trial, basically, and he's done his shoulder," Blackadder told the Bath Chronicle. "We were going to see what he was like and make a decision.
"Because he's dislocated his shoulder on our watch, we'll look after him. We think that's the right thing to do. It could be a six-month injury."