The opening batsman, who leads Australia in the shortest format of the game, injured his left hamstring while trying to complete a quick single in the second T20 match against India in Melbourne on Friday.
The 29-year-old has a history of hamstring problems and required surgery after a sustaining a tear while playing for Mumbai in last year's Indian Premier League T20 competition.
"Aaron had scans on his injured left hamstring that confirmed a moderate grade hamstring injury," Cricket Australia physiotherapist Alex Kountouris said in a statement.
"This is not a recurrence of the previous hamstring injury that required surgery in April 2015. Although this current injury doesn't require surgery there is a period of rehabilitation required before he can resume playing.
"We are aiming to have Aaron fit for the ICC World T20 in India but will have better idea about his fitness for that tournament in the coming weeks once we see how he responds to treatment and a rehabilitation programme."
Finch missed the third T20 match against India, which the touring side won to sweep the series 3-0, and was also left out of Australia's squad for three one-day internationals in New Zealand this month.
Australia, who have never won the World Twenty20, have been drawn with New Zealand, India, Pakistan and a yet-to-be-confirmed qualifier in Group 2 of the Super 10 round.
The tournament will be played from March 8-April 3.
(Reporting by Sudipto Ganguly in Mumbai; editing by Peter Rutherford)
