Finch initially suffered the injury to his right knee during practice ahead of the T20I series against West Indies and aggravated it in the final match in St Lucia. He was subsequently ruled out of the start of the ODI series and the decision was taken on Saturday that he would now return home to Australia instead of continuing to Bangladesh.
"I'm extremely disappointed to be heading home," Finch said. "This was considered the best course of action rather than travelling to Bangladesh, not being able to play and losing that recovery time. I will have the surgery if required and start the recovery process ahead of the World Cup."
A Cricket Australia statement added: "Selectors and the Cricket Australia medical team are optimistic Finch will recover in time for the ICC T20 World Cup in the UAE and Oman, which commences in mid-October."
Finch will undertake two weeks of quarantine when he arrives back in Australia which takes him up to the second week of August and leave around two months for him to be fit for the World Cup, although it remains to be confirmed when the squad will depart for the UAE.
Alex Carey will continue as ODI captain for the deciding match of the series against West Indies on Monday with the selectors to decide on who will lead the T20I team in Bangladesh closer to the start of those matches on August 3.
Due to the complexities around travel arrangements and biosecure bubbles, Australia won't call up a replacement for Finch. They have two reserve players on the tour, but paceman Nathan Ellis and legspinner Tanveer Sangha only provide bowling cover.
When Finch missed a T20I against India last season, Matthew Wade led the side. Carey is not a certain starter in the T20I side unlike he is the one-day set-up. Other options could include the in-form Mitchell Marsh or the experienced Moises Henriques.
In the short term Finch's injury leaves Australia without another senior player on a trip where they are already missing David Warner, Steven Smith, Glenn Maxwell, Marcus Stoinis from a likely first-choice batting line-up.
It will likely mean another chance to open for Josh Philippe who was used in the middle-order at the start of the West Indies series before going back to the top, the position he holds for the Sydney Sixers in the BBL, in the final game of the series, though, he made a duck.
Throwing further forward to the World Cup, while there is optimism that Finch will be fit, it does open the possibility of Pat Cummins, the official vice-captain across formats, leading Australia at the tournament.