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."
Gilbert has released a new line of rugby cleats. The Gilbert Virtuo 8S is part of the exciting new product. Check it out.
The Barbarians are one of the top invitational rugby sides with a long history and classic rugby jersey.
The Nike Tiempo is a solid rugby cleat and one of few styles still made from full-grain natural leather.
The Lions get ready for their matches with this green training jersey. It's what the players wear. Get in the Gear!
A cool looking all black rugby cleat with the high performance adidas is known for. Get in the Gear!
Wear the crest of the British and Irish Lions on your t-shirt. A great look for the summer.
$29.99
The Lions are ready to get their Australia tour underway. They arrive in Perth on Monday.
The New Zealand All Blacks training jersey for 2013/14. Get in the Gear!
The USA Rugby Pro Alternate rugby jersey is perfect for any fan of the Eagles. Get yours to wear during the summer Test matches.
The NEW All Blacks 2013/14 jersey has arrived at World Rugby Shop. Dare to wear the colors of the All Blacks.
