Coast listener Grant Avery complained about the broadcast of the song - which was released in 1976 - claiming its use of the word "nigger" was "offensive, racist and unacceptable".
The song includes the lyrics:
"To the white folks who watched he was a revolutionary bum / And to the black folks he was just a crazy nigger / No one doubted that he pulled the trigger."
Avery believed the broadcast breached the good taste and decency and discrimination and degeneration standards of the Radio Code of Broadcasting Practice.
Hurricane is a protest song written and released in early 1976 by Dylan about the imprisonment of former professional boxer Rubin Carter, later portrayed in the Denzel Washington film The Hurricane.
The song is more than eight minutes long and cites alleged acts of racism and profiling against Carter, which Dylan sings as leading to a false trial and conviction.
Avery said the song could cause a "significant amount" of damage to society and individuals and Coast must recognise the change in society since its release.
"The song and Bob Dylan's use of this word is nearly 50 years old," he said.
"The acceptability and tolerance of the word that existed 50 years ago in society does not exist today."
However, content director of Coast, Mix and iHeartRadio David Brice said the song was hugely significant in New Zealand.
"I completely concur from where the BSA was coming from in terms of the severity of people's discomfort in use of the word," he said.
"But why I thought we had to contest the complainant's view was because of the history of the song and the fact it was used in the context of African Americans.
"I thought the perspective the complainant was coming from was all wrong - it's not a word which should be used but in the context of that song, it is what it is."
The authority agreed, deciding not to uphold the complaint following careful consideration, stating "this decision has not been made lightly".
"The song itself has social and historical significance and tells a story of racial injustice and inequality experienced by African Americans in the 1960s," it said.
"It could be argued that the song itself is an example of the power of the right to freedom of expression.
"The language and expressions used is integral to the narrative of the story told through the song."
The authority also dismissed two complaints against comments Newstalk ZB host Leighton Smith made about climate change and one complaint about comments about biased media.
