Chief executive Tim Jordan said flights had been temporarily suspended in a brief statement.
"Discussions are currently underway regarding the ongoing viability of the business," Mr Jordan said on Tuesday.
"We apologise to our customers who are impacted by this and we're working as quickly as possible to determine a way forward that ensures there is ongoing competition in the Australian domestic aviation market."
Tim Jordan has cast doubt on the viability of the budget domestic airline. (Lukas Coch/AAP PHOTOS)
Flights suspended on Tuesday include those to or from Melbourne, the Sunshine Coast, the Gold Coast, Launceston, Alice Springs and others.
Federal Transport Minister Catherine King said a hotline for stranded passengers would be created.
Qantas and Virgin airlines "stand ready to assist" passengers who need to get home, she said.
"My department has reached out to Bonza and our expectation is that they keep passengers informed of their options and their consumer rights," Ms King said.
Virgin Australia, Qantas and Jetstar have offered to fly Bonza passengers free of charge to airports closest to their destination.
Jamie Taylor, her husband and three young children found out their flight from the Gold Coast to Launceston was cancelled once they had reached the gate on Tuesday morning.
She said the family of five has since spent more than $3000 to find a new way home.
They drove a hire car down to Brisbane to catch a new flight to Sydney, where they will stay in a hotel for a night before finally flying back home on Wednesday.
"I've been in tears a couple of times," Ms Taylor told AAP.
"My kids are missing an extra day of school than we planned."
Catherine King says a hotline will be created to help stranded Bonza passengers. (Mick Tsikas/AAP PHOTOS)
Passenger Glenn Stacey left his accommodation at 4.30am to catch a flight from Launceston to the Gold Coast and had just two hours notice his journey would be cancelled because of "operational requirements".
He was meant to work on Tuesday afternoon but won't make his shift as the only flight he could secure is scheduled to leave at 5.30pm and cost him $500.
"I've now got to sit around at the airport all day," Mr Stacey said.
The Sunshine Coast-based company was unveiled in October 2021 and operated its first flight in January 2023.
It originally flew 27 routes to 17 destinations but started cutting services during its first six months.
Bonza flies Boeing 737-Max-8 planes and is backed by 777 Partners, an investment group based in Miami, Florida.
Earlier in April, the Australian Financial Review newspaper reported advisory firm KordaMentha had been called in to help the company, which Bonza denied.
Bonza's LinkedIn profile states it has between 51 to 200 employees.
Bonza was unveiled in late 2021 and operated its first flight in January 2023. (HANDOUT/Moment RF)
The airline operates flights from select airports on Australia's east coast but does not have flights to or from Sydney and Brisbane.
It flies to many regional destinations including Albury, Mildura, Mount Isa, Tamworth and Port Macquarie.
The Transport Workers' Union says Bonza's uncertain future points to a "broader issue of instability in aviation" and repeated calls for greater regulation of the industry.
National Secretary Michael Kaine said it was an extremely distressing time for passengers and workers.
"Bonza must ensure staff are prioritised and informed as this process plays out," he said.
AAP has contacted 777 Partners and KordaMentha for comment.
6°C