Chief executive Tim Jordan says flights have been temporarily suspended.
"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.
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 to cut back 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.
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.
Virgin Australia is offering stranded Bonza passengers free flights.
"We will immediately support any passengers stranded mid-journey by offering complimentary seats on Virgin Australia-operated flights to the airport nearest to their final planned Bonza destination," the company said on social media.
AAP has contacted 777 Partners and KordaMentha for comment.
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