Sheridan had scans on his left shoulder after England's 13-9 victory over Argentina and surgeons back in the UK, who studied the images, ruled him out of the tournament.
The Sale prop had battled back from reconstructive surgery on his right shoulder to make the World Cup squad.
England's management are waiting for tournament organisers to officially ratify Sheridan's departure before settling on the identity of a replacement.
Sheridan has already undergone two operations on his left shoulder after injuring the same shoulder he dislocated badly in 2009.
The 31-year-old is not yet sure whether he will require more surgery.
"It's a big blow to leave the World Cup through injury, but it's a significant injury to the shoulder, so I have to deal with that and get on with it now," said Sheridan.
"I didn't know the exact incident that had caused it during the game; initially it just felt a bit sore, but a couple of days post-match it was still pretty painful and that's when I had the scan on it.
"I think everyone knows shoulders are quite complicated structures, so it's difficult to come back.
"It takes a lot of work and a lot of work from the physios and the conditioners as well to get players back from shoulder injuries.
"But we are where we are and you just have to get on with it and see what the results are after I've seen the specialist.
"I have to wait until I get back home and see the surgeon - I am quite well acquainted with him now.
"He will give me some good advice and see if I need an operation and what the next stage is."
England selected five props in their 30-man squad and have the resources to cover for Sheridan's absence against Georgia this weekend.
Alex Corbisiero is the only other specialist loosehead in the squad and is likely to make his World Cup debut on Sunday, but Matt Stevens and David Wilson are capable of playing both sides.
"Sheri worked really hard over the summer to come back from injury and has put in two very good performances. It is very disappointing," Corbisiero said.
"I just wish him all the best. He's a world-class player. He's a big hero of mine. I think the squad will miss him, but we've just got to get on with it now and go forward as a team in the tournament.
"When my opportunity comes I'll be ready to take it and make the most of it.
"Responsibility will fall on all of us, as a front row, as a pack. There's four of us (props) left here and it's going to be a big job for all of us.
"Losing someone with the experience of Sheridan is tough, but it will make us stronger and pull together. We have four good players there."
Corbisiero made his Test debut against Italy in the Six Nations after Sheridan had pulled out with a calf injury.
"I've learned a lot from Sheri. He has been through a lot," said the London Irish prop.
"He has played in a lot of tough games, he's played Lions, he's a big carrier, he's got a great workrate for a big guy and his set piece is very effective as well.
"He was helpful to me, but it wasn't like taking me under his wing - there was mutual respect and he is more than willing to talk to you and to help you out.
"He's a great guy. I just feel for him."
It was not a good 24 hours for England.
Sheridan's exit came the morning after England manager Martin Johnson heard Courtney Lawes had received a two-week ban for striking Mario Ledesma with his knee.
"It's really sad for Sheri. He has been unlucky with injuries and we wish him all the best for his recovery," Johnson said.
"We brought five props so we have options there and we can bring another player out, but we will decide what to do about that in due course."
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