The 26-year-old will miss the double header with former Heineken Cup winners Brive in December as well as the Round 5 and 6 clashes with Petrarca and El Salvador.
"Dave's probably going to be out for between 10 and 12 weeks because of his shoulder injury," said Sale's director of rugby Mike Brewer told the Manchester Evening News.
"He's basically got a labral tear and he will need quite a serious shoulder operation.
"It's a big blow for us. He'll be having surgery next Wednesday and will be out until February."
The news is a third piece of bad luck for the Sharks after they lost captain James Gaskell and prop Eifion Lewis-Roberts to long-term injuries earlier this season.
Brewer intends to bring in a replacement for former Saracens flanker Seymour as soon as possible, with the New Zealander admitting he will be casting his net far and wide to bring in a player of the required quality.
"At least the timing of the injury helps because the Currie Cup in South Africa finished last weekend and the ITM Cup finishes this weekend over in New Zealand, so those competitions ending allows us to go and look down there," added Brewer.
"And then really it's a matter of also looking around in Europe and seeing if there is anyone of that quality who is not getting rugby or who has fallen out with whoever, so we'll see what's available.
"So I am talking at the moment about getting in a openside flanker on a short-term basis. The idea is that we'll try and get someone in on a three month contract and I've already got one or two irons in the fire as regards a short-term replacement.
"Finding a replacement openside flanker has now become more of a priority than bringing in a prop to cover for Eifion's injury. The prop position is a concern but losing Dave is a big loss."
Sale began their Amlin Challenge Cup season in the perfect manner, with two bonus-point wins in their opening two fixtures giving them maximum points a third of the way through the group stages.
December's home and away ties with 1997 Heineken Cup winners Brive are likely to decide Sale's fate as they look to match their Challenge Cup winning triumphs of 2002 and 2005.