The 31-year-old, who suffered a similar problem last season, was due to undergo surgery on the injury on Monday and his absence will be a big blow to the Chiefs as he has been near ever-present on the loosehead side of the scrum this season.
Head coach Rob Baxter said: "Sturge has broken his arm and he'll be having an operation. It's a similar injury to the one he suffered last time but the other arm this time. He's likely to be out for eight, 10 or 12 weeks - it's a relatively serious injury."
But Baxter is hopeful his side can cope with the loss of Sturgess as they look to again secure Heineken Cup qualification.
"It's unfortunate for Sturge because the season has been going well for him, but at the same time it's an opportunity for someone else," he said.
"Ben Moon went on and did well, Carl Rimmer came to us originally as a loosehead so there's an opportunity there for him to get some more time in his preferred position.
"Luke Cowan-Dickie is playing very well down at Plymouth at loosehead so we've got options.
"We do feel we've got a strong squad here so at times like this the guys have got to stand up and come in and do a good job for us."
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