A 48-year-old man at the scene was arrested after he allegedly climbed aboard the bus in Brisbane before "throwing some type of incendiary device at the driver", Xinhua news agency quoted Queensland Police Commissioner Ian Stewart as saying in Brisbane.
"Sadly the driver, Manmeet Alishera, 29-year-old man, died as a result of his injuries," Stewart said.
There is no evidence of any linkage to "terrorist type activities" or links to a racial motivation, Stewart said.
"While we don't know the motivations at this stage, I want to reassure the community that we take these incidents very seriously," Stewart said, adding counter-terror authorities were initially involved.
Local media reported that Manmeet Alisher was a beloved Indian singer and prominent figure in Brisbane's Punjabi community.
He was described as a soft spoken, courteous and genuine man.
Several passengers on board the bus at the time managed to escape via the rear doors "partly because of the heroic actions of a taxi driver who saw what was unfolding", Stewart said.
Six people were taken to hospital for smoke inhalation and minor injuries.
Queensland has been in mourning over the past week following the deaths of four people in Australia's largest amusement park Dreamworld and the murder of a woman in Brisbane.