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Smith, 35, previously served a two-year ban from captaincy following his involvement in the 2018 ball-tampering scandal.
Cummins is missing the series for the birth of his second child and seamer Josh Hazlewood is also left out as he recovers from a calf injury.
Spin-bowling all-rounder Cooper Connolly earns his first Test call-up while Nathan McSweeney, who opened in the first three Tests in the recent series against India, retains his place.
McSweeney, 25, scored 72 runs in six innings before being replaced by 19-year-old Sam Konstas, who is also named in the squad.
Connolly, 21, has played two one-day internationals and two T20s for Australia and is yet to take a wicket in either format.
He joins Nathan Lyon, Matt Kuhnemann and Todd Murphy in the spin attack, while Mitchell Starc, Scott Boland and Sean Abbott are the frontline seamers.
All-rounder Mitchell Marsh has also been omitted after a poor series against India while Beau Webster, who replaced him in the final Test at Sydney, keeps his spot.
The first Test takes place on 29 January in Galle.
Australia's series win over India saw them qualify for the World Test Championship final, where they will take on South Africa at Lord's on 11-15 June.