Powell's ban comes less than a month after Port Adelaide's Jeremy Finlayson was given a three-game ban for his homophobic verbal abuse of an Essendon player and ordered to undertake Pride in Sport training.
The AFL said Powell's slur used in the Suns' loss at the Gabba on Sunday "demeans and denigrates any person regardless of their sexuality".
Powell's ban was longer due to the proximity of the two incidents and the AFL wanting to deter such conduct.
"It is extremely disappointing to be dealing with a similar incident in only a matter of weeks," AFL general counsel Stephen Meade said in a statement.
"The AFL acknowledges Powell's remorse and co-operation, and while it has considered the circumstances in which the comment was made, there are no excuses for this conduct in our game.
"We foreshadowed both publicly and privately that after what transpired at Gather Round if a similar incident was to happen there would be further consequence.
"There could be no clearer message - homophobia has no place in our game, nor in society.
"We want all people in the community to feel welcomed in our game, and comments such as Powell's only takes away from this. As a code, as a community, we all must be better."
It is the third incident of homophobic language this year.
North Melbourne coach Alastair Clarkson was fined $20,000 and received a suspended two-game ban for his pre-season tirade towards St Kilda duo Jimmy Webster and Dougal Howard.
The Suns said Powell apologised to the Brisbane player during the game, at the conclusion of the game, and again in the hours after the match.
"As soon as the word came out of my mouth, I knew I had made a terrible mistake," Powell said in a statement.
"I have offered my apology to the Brisbane player and would like to publicly apologise for my comment. I will take full responsibility for what I said.
"I know there is no place for comments of that nature and I will accept the repercussions for my actions. I should have known better and I need to prove this with my actions moving forward."
The Suns condemned Powell's actions as "completely unacceptable", but said they would provide "guidance and education" during his suspension, when he cannot play VFL or AFL.
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