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White, who had a poor World Cup with the bat and was dropped during Australia's one-day series in Bangladesh, was replaced by Shaun Marsh in the squad named on Wednesday.
"Cameron White is unlucky to be omitted from the one-day squad having been a regular and successful member of the squad for the last few series," Australia's chairman of selectors Andrew Hilditch said in a statement.
"Cameron lost his position in the side during the recent one-day tour of Bangladesh but the NSP (National Selection Panel) is confident that he will force his way back into the team through weight of runs."
Doug Bollinger was recalled to the Michael Clarke-led one-day side with fellow paceman Shaun Tait opting out of 50-over cricket following Australia's quarterfinal exit from the World Cup in the subcontinent.
Former test and one-day skipper Ricky Ponting and veteran batsman Mike Hussey have retained their places in the one-day side, while fast bowler Brett Lee keeps his spot in the Twenty20 side.
Australia will play two Twenty20 matches, five one day internationals and three Tests during the seven-week tour of Sri Lanka.
The Test team would be named later in July, Cricket Australia said.
Twenty20 squad:
Cameron White (captain), Shane Watson (vc), Aaron Finch, Brad Haddin, John Hastings, David Hussey, Mitchell Johnson, Brett Lee, Shaun Marsh, Stephen O'Keefe, James Pattinson, Steven Smith, David Warner.
One-day squad:
Michael Clarke (captain), Shane Watson (vc), Doug Bollinger, Xavier Doherty, Brad Haddin, John Hastings, David Hussey, Michael Hussey, Mitchell Johnson, Brett Lee, Shaun Marsh, James Pattinson, Ricky Ponting, Steven Smith.
