Left-handed batsman Usman Khawaja has replaced Finch in the squad for Sunday's match and has also been included in Australia's one-day international squad for the tour of New Zealand
All-rounder Shane Watson will lead Australia in the third and final Twenty20 international against India on Sunday in the absence of Aaron Finch, who was ruled out after damaging his left hamstring during Friday's second match in Melbourne.
Left-handed batsman Usman Khawaja has replaced Finch in the squad for Sunday's match and has also been included in Australia's one-day international squad for the tour of New Zealand.
"It is an honour to be asked to lead the side on Sunday, although the circumstances are far from ideal," Watson said in a Cricket Australia statement.
"We may have lost the series but there is a great deal to play for with the ICC World Twenty20 coming up and you can be sure we will be determined to do well in Sydney."
The 34-year-old Watson has previously captained Australia in a lone Test and nine ODIs and is the country's second most experienced player in T20 internationals behind opening batsman David Warner.
The all-rounder is Australia's leading wicket-taker in the T20I format with 41 victims and his tally of 1191 runs is second only to Warner's haul of 1465 for his country.
Image: Australia's Shane Watson
Photograph: Robert Prezioso/Getty Images
Why Shane Watson is a worried man...
Injured Finch to miss 3rd T20; Khawaja to replace him
India seal T20 series after big win at MCG
Dhoni lauds bowlers after T20 series win over Aus
PHOTOS: Rohit, Kohli power India to series win in Melbourne