The 24-year-old suffered a side strain in the one-day Tri-series final against England two weeks ago and missed Australia's opening win over the same team in Melbourne on Saturday.
"I'm no chance for Bangladesh, I can tell you that," Faulkner told reporters in Brisbane on Monday.
"Time's sort of flown a bit, but hopefully I'm back sooner rather than later," he added.
Faulkner has been batting in the nets with no discomfort and said he expected to resume bowling this week.
"I haven't been given any fitness deadline, I'm not sure what their (the selectors') plan is with that," he added.
"I'll just do as I'm told with the medical staff and concentrate on that. It's rehab 24-7 for me and will continue to be until I'm back."
Faulkner's continued absence may ease the pressure on fellow fast bowling all-rounder Shane Watson, whose place is under scrutiny after he was out for a golden duck and failed to take a wicket against England.
Mitchell Marsh, Australia's third pace bowling all-rounder, picked up the slack with a career-best haul of 5-33 from his nine overs, suggesting the World Cup co-hosts should be well covered for the Bangladesh game at the Gabba ground.
The enduring faith in Watson has proved controversial in recent years, with pundits questioning the 33-year-old's value amid a string of disruptive injuries and inconsistent performances with bat and ball.
Marsh, however, backed the barrel-chested Queenslander, who came into the tournament boasting the second best batting average at World Cups among participating players behind his captain Michael Clarke.
"He's still the premier all-rounder in our team and a vital cog for us at this World Cup," Marsh said on Sunday.
"All of us know how important he is."
Faulkner said he did not think he was battling Marsh for a single all-rounder spot lower down the batting order.
"I don't think we're actually fighting for the same sort of spot, we're different players," he added.
"Mitch has always been a batter and his overs have been handy. I know he's working hard on his bowling and he got some rewards the other day.
"I think we can both definitely play in the same team and we have a few games so far so there's no reason we can't continue."
(Reporting by Ian Ransom; Editing by Nick Mulvenney)
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