Brown, who guided the club into the Football League with three promotions in five years, bade an emotional farewell to supporters following the 1-0 home defeat by Torquay, their sixth loss in seven matches.
Brown waved to all four sides of their Kingsmeadow ground before heading to the dressing room, where assistant boss Stuart Cash revealed he was in tears.
Cash has also left the club with Simon Bassey placed in caretaker charge.
In a club statement, chief executive Erik Samuelson said: "This is a terribly sad moment for all of us.
"Terry has been a wonderful manager and a fantastic ambassador for the club since we appointed him over five years ago.
"He and Stuart guided us from the Ryman League into the Football League and for that we will be forever grateful. On behalf of everyone at the club and all the fans, I'd like to thank them for everything they have done for us."
Brown, 60, took over the Dons in May 2007 and led them to back-to-back promotions to the Conference.
They then reached the Football League for the first time via the play-offs in 2011, just nine years after holding trials on Wimbledon Common to form a new team following the original Wimbledon's controversial switch to Milton Keynes to become MK Dons.
AFC finished 16th in League Two last season but are currently fourth from bottom with just four points from seven matches.
Brown said: "Last night was a special moment as not many managers get to leave in such a way by saying goodbye to the supporters.
"Stuart and I felt that we had to get a couple of wins out of our home games and that if we lost both games then we would no longer be at the club.
"That is sad, but I will remember five absolutely fantastic years at the club. I cannot say I have enjoyed this season as it has not gone well, but my abiding memory will be our three promotions."
Lawrie Sanchez, the old Wimbledon's FA Cup final goalscoring hero in 1988, could be among the frontrunners for the role while former Brentford boss Andy Scott was spotted in the crowd on Tuesday night.