Mitchell - who has 15 Wales caps and has also played for Ospreys, Exeter and Cardiff Blues - has been at the Rec on a short-term deal since being released by Dragons last May.
Bath director of rugby Todd Blackadder said Mitchell's injury could sideline the 31-year-old for up to six months.
"We got Craig on trial, basically, and he's done his shoulder," he said.
"We were going to see what he was like and make a decision."
Mitchell made his Test debut against Canada in 2009 and went on to play for Wales during the 2011 World Cup.
He played 11 times for Dragons last season and had seemed set to join the sizeable Welsh contingent at Bath that includes fellow internationals Taulupe Faletau, Luke Charteris, Rhys Priestland and Aled Brew, plus backs and skills coach Darren Edwards.
But Blackadder, speaking to the Bath Chronicle, said the English Premiership club had a duty of care for the stricken player.
"Because he's dislocated his shoulder on our watch we'll look after him," Blackadder added.
"We think that's the right thing to do. It could be a six-month injury."
Wales tight-head prop Craig Mitchell has suffered a long-term shoulder injury while training with Bath.