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It was initially hoped the injury was just bruising and swelling but X-rays have discovered a more serious verdict.
"It is a blow to lose somebody like Charlie but he should be back in around three weeks, maximum four," said Sale director of rugby Kingsley Jones.
Hodgson joins Eifion Roberts, Neil Briggs, David Seymour, Tom Brady, Aston Croall and James Gaskell on the mid-to-longer term injury list at the Manchester based club.
Sale and Brive sit at the top of Pool 2, level on points and the English side travel to the South of France for the first of the two fixtures this weekend.
