The 36-year-old wants to concentrate on his career as a manager.
Brown joined Aberdeen on a two-year contract after leaving Celtic at the start of the season.
Brown joined Celtic from Hibernian in 2007 and won 10 Scottish league titles, six Scottish league Cups and six Scottish Cups.
Brown made 33 appearances in all competitions for Aberdeen this season and scored two goals.
He said: "I would like to take this opportunity to firstly thank the board at Aberdeen and, of course, Stephen Glass and his backroom staff for giving me the opportunity to enjoy my first taste of coaching.
"I'd also like to thank all my team-mates and the great staff both at Cormack Park and Pittodrie.
"I know I was only in the north east for a short period, but the fans made me feel welcome from day one, so my thanks must also go to them for showing me so much support.
"Aberdeen is a huge club and I know there is a real determination from all to deliver success both on and off the pitch. I wish them all the best for the remainder of the season."
Brown won 55 caps for the Scotland national team.
