The 33-year-old was hurt during Gloucester's opening Aviva Premiership game of the season against Northampton.
After almost three months of rest and rehabilitation, Brown underwent complex surgery on nerve damage, but although the operation will improve his shoulder movement, it has meant an end to his playing career.
"It is stating the obvious, but I am totally gutted," he told the club's official website.
"When the surgeon came in after the operation and told me that I would not be able to play rugby again, the news hit me hard and has been tough to deal with, especially as there has been a new dawn at Gloucester under (rugby director) Nigel Davies and I so wanted to be part of it.
"I genuinely thought that I had a few good years left in me, but it's not to be. I've had to take on board the advice I have received and what my body is telling me."
Brown won three England caps in 2006 and 2007, and he made 227 Premiership appearances, including a competition record 87 consecutive starts.
"I've been incredibly lucky to spend so many years playing in the top flight, firstly with my home town team, Bristol, and then to play for so many memorable years at Gloucester," he added.
"I have still got lots of things to focus on and enjoy for the rest of the season - my continued work with the team and the testimonial activities that the committee have kindly organised for this year.
"It will give me an opportunity to thank everyone who has been so good to me over the years."
David Barnes, rugby director of the Rugby Players' Association, paid tribute to Brown.
"Alex is one of the most respected players across the Premiership for his commitment, professionalism and his understanding of the game," Barnes said.
"The irony is not lost on us that this year Alex has generously been supporting Restart - the Rugby Players' charity - to help other players who have suffered serious injury and illness, and now he too finds himself in this position.
"We will continue to work closely with Alex as he begins to plan the next stage of his life."
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