Browne, 28, was knocked out by Filipino fighter Carlo Magali in the last round of Friday's bout for the IBF super-featherweight belt in Sydney.
The father of two was in a coma, having been taken to hospital after receiving treatment at the end of the fight.
Browne's death comes just six months after Braydon Smith died shortly after a bout in Toowoomba, and AMA vice-president Stephen Parnis believes the sport should not continue.
"One punch can kill - whether you are outside a pub on a Friday night or in a boxing ring - and this is the thing that causes young lives to be ended so traumatically," he told ABC.
"People need to be careful and they need to think twice about participating in this sport.
"It's a terrible tragedy for a young man with a young family, but the fact that is was entirely avoidable just leaves a real sense of bitterness.
"I know they don't intend for this to happen. The way that boxing is designed there will be these times inevitably where someone will get bleeding or irreversible damage to the brain and they will either lose their life or end up with brain damage.
"That is why the AMA thinks that we cannot continue with it (boxing)."