Mitchell picked up the injury after coming on as a replacement for Exeter's second team last Monday night, with head coach Rob Baxter since confirming that the 27-year-old is set for a lengthy spell on the sidelines.
"Mitch is looking a pretty long-term injury," said Baxter, after Exeter produced a late comeback to beat London Irish at the Madejski Stadium on Saturday.
"We haven't finalised the exact issue with Craig yet, but he is likely to require an operation on his shoulder / pec area - an injury very similar to what he did playing for us up at London Welsh last year. His absence is likely to be quite lengthy."
The news is a bitter blow to Mitchell, who told this website last month that he was keen to feature for his country when the South Africans arrive in Cardiff on November 9.
The former Ospreys front rower was hoping a strong start to the season would earn him a squad spot against the Springboks but those aspirations have now been all but dashed after yet another injury setback.
Mitchell missed the opening summer Test against Japan with ankle trouble, having also been absent for each of the last set of Dove Men Series Tests with a ruptured bicep.
He fought back from last season's autumn disappointments to feature against Ireland, France and Italy in Wales' triumphant RBS 6 Nations campaign but now looks like having to wait until at least next year's tournament to add to his tally of international caps.
Tickets to see Wales in action against South Africa, Argentina, Tonga and Australia at the Millennium Stadium in the 2013 Dove Men Series are available now online at www.wru.co.uk/tickets with prices from £25, £10 concession.
Wales' Dove Men Series 2013 Fixtures
Wales v South Africa
Saturday, 9 November, Kick-Off 5.30pm - £70 / £60 / £40 / £25
Wales v Argentina
Saturday, 16 November, Kick-Off 2.30pm - £40 / £30 / £10 concession (U16) /£70 Family ticket 2 adults + 2 concession
Wales v Tonga
Friday, 22 November, Kick-Off 7.30pm - £25 / £10 concession/ £60 Family ticket 2 adult + 2 concession/ Minis/Juniors/Schools offer, with every 8 concessions purchased 2 adult tickets free
Wales v Australia
Saturday, 30 November, Kick-Off 5.00pm - £70 / £60 / £40 / £25