Perth father Cameron Hughes, 39, was taken into custody on Friday accused of breaching visa conditions after separating from his wife.
He shared an eight-year-old son with her and had reportedly been living in Bali for 15 years, where he ran a car restoration business.
Mr Hughes was awaiting deportation at the Ngurah Rai Immigration Office on the island when he was found unconscious and unresponsive in a bathroom attached to his cell.
First aid was then administered and he was transferred to a local hospital but died of a suspected heart attack on the way to the facility, Ngurah Rai Immigration Office said in a statement.
The family of Mr Hughes described him as a "beautiful person" in a statement given to the ABC, saying there were unanswered questions about the circumstances of his detention and cause of death.
"We will be working closely with consular staff to understand what actually happened, and work with them to understand the full extent of the situation," the family said.
Western Australian Premier Roger Cook thanked Australian consular officials for assisting the family.
"Our understanding is that he was taken into custody on a visa-related matter, and during that custody, he had a medical episode and lost his life," Mr Cook told reporters on Monday.
"Our heart goes out to him. This is a really sad situation."
The premier also called for a probe to ensure there was no foul play involved, and to provide closure to the family.
"We hope a thorough investigation will take place just to ensure Mr Hughes didn't come to any mistreatment while he was in custody."
Mr Hughes had been routinely checked and monitored via CCTV while in his cell, Bali immigration officials said.
"Further investigation into the cause of death is the responsibility of the police and the relevant hospital," the Ngurah Rai Immigration Office statement said.
Mr Hughes was resilient, hardworking and "proud of overcoming challenges to build a good life", his family said.
"Taken too soon doesn't even come close. We are completely broken as a family," they said.