Finch had been battling back spasms and a side strain which kept him out of domestic first-class and one-day matches over the past week.
But after batting in the nets on Saturday at Adelaide Oval, Finch says he's fine to lead Australia in the opening match of the men's international summer.
"I was a bit worried about throwing yesterday," he said. "It didn't progress all that quickly but ... the last three days it has been really good. I feel confident to go."
Sunday's match marks the start of Australia's preparations for the Twenty20 World Cup to be held in Australia from mid-October next year. The Australians, ranked fifth in T20 cricket, have 21 T20 fixtures between now and the start of that tournament.
"Everyone has talked it to death about the fact that we haven't performed at our best in international T20s, whether it be series or World Cups," Finch said. "So it's a real focus for us to be able to have the continuity of selection over the next 12 months."
Sri Lanka and Australia play a second T20 match on Wednesday in Brisbane, followed by the third on Friday in Melbourne.
Australia then hosts Pakistan in a three-match T20 series with games on Nov. 3 in Sydney, Nov. 5 in Canberra and Nov. 8 in Perth.