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.
Spinner 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.
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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.
Australia Test squad for Sri Lanka: Steve Smith (capt), Sean Abbott, Scott Boland, Alex Carey, Cooper Connolly, Travis Head, Josh Inglis, Usman Khawaja, Sam Konstas, Matthew Kuhnemann, Marnus Labuschagne, Nathan Lyon, Nathan McSweeney, Todd Murphy, Mitchell Starc, Beau Webster.
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