Australia have picked three pacemen for the first T20 international against Sri Lanka on Tuesday, hoping their World Cup-winning formula will work in their favour again.
With conditions in Colombo likely to suit fast bowlers, Kane Richardson is recalled for the rested Pat Cummins and joins Mitchell Starc and Josh Hazlewood in the attack.
Cummins and Zampa are the only absences from the XI that won the world title in Dubai last year.
Finch said that he had been tempted to pick a second spinner, but decided to stick with one because of the conditions in Colombo.
"The square is quite green, there's been a lot of rain and the outfield is heavy," Finch said on Monday.
"We expect a little spin, but it's not a dry surface by any stretch, that's the reason for picking one spinner."
Allrounders Glenn Maxwell, Mitch Marsh and Marcus Stoinis will fill the fifth bowler's role.
David Warner and Steve Smith are back in the side after missing Australia's recent T20 matches.
Australia are on a seven-week tour of Sri Lanka, even as the island nation wrestles with an economic crisis and recent unrest.
The Australians will play three Twenty20 internationals, five one-day internationals and two Test matches during the tour, which ends July 12.
Australia XI: Aaron Finch (c), David Warner, Mitch Marsh, Glenn Maxwell, Steve Smith, Marcus Stoinis, Matthew Wade, Ashton Agar, Mitchell Starc, Kane Richardson, Josh Hazlewood.
Sri Lanka squad: Dasun Shanaka (c), Pathum Nissanka, Danushka Gunathilaka, Kusal Mendis, Charith Asalanka, Bhanuka Rajapaksa, Nuwanidu Fernando, Lahiru Madushanka, Wanindu Hasaranga, Chamika Karunaratne, Dushmantha Chameera, Kasun Rajitha, Nuwan Thushara, Matheesha Pathirana, Ramesh Mendis, Maheesh Theekshana, Praveen Jayawickrama, Lakshan Sandakan. Standby: Jeffrey Vandersay, Niroshan Dickwella.