The 27-year-old has had a poor recent run of form and was replaced for the one-dayers by Shaun Marsh, who missed the World Cup earlier this year due to injury.
Australia play two Twenty20 matches, five ODIs and three Tests against Sri Lanka from August 6-September 20, with the Test team to be released later this month.
'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,' said chairman of selectors Andrew Hilditch.
'Cameron lost his position in the side during the recent one-day tour of Bangladesh but the selectors are confident that he will force his way back into the team through weight of runs.'
Young paceman James Pattinson and bowling all-rounder John Hastings have been included in both squads while veteran fast bowler Brett Lee retains his spot in the Twenty20 team.
'Taking on the talented Sri Lankan team on their home soil in all forms of the game is always challenging but we also see it as an exciting opportunity for both the Twenty20 and one-day squads,' said Hilditch.
Selectors called the Twenty20 squad well balanced with potentially explosive batsman Marsh, Shane Watson and David Warner at the top of the order combined with White, Aaron Finch and David Hussey in the middle order.
Pattinson will spearhead the bowling along with Lee and Mitchell Johnson. Marsh is expected to open the one-day batting, with former captain Ricky Ponting also in the side.
'Shaun can open the batting but also provides flexibility throughout the order and gives the squad great balance,' said Hilditch.
ODI squad: Michael Clarke (capt), Shane Watson (vice-capt), Doug Bollinger, Xavier Doherty, Brad Haddin, John Hastings, David Hussey, Michael Hussey, Mitchell Johnson, Brett Lee, Shaun Marsh, James Pattinson, Ricky Ponting, Steven Smith.
Twenty20 squad: Cameron White (capt), Shane Watson (vice-capt), Aaron Finch, Brad Haddin, John Hastings, David Hussey, Mitchell Johnson, Brett Lee, Shaun Marsh, Stephen O'Keefe, James Pattinson, Steven Smith, David Warner.