Symonds was left out of the one-day side for the three-match series with Bangladesh in Darwin earlier this month after he missed a team meeting and went fishing instead.
"Andrew Symonds was stood down for disciplinary reasons in Darwin and is now going through a process...designed to give him time to assess whether he is fully committed to all of the things needed for a cricketer to be a member of the world's number one team," chairman of selectors Andrew Hilditch said in a statement.
The 33-year-old had been in trouble with team officials previously and was almost sent home from the 2005 Ashes tour of England when he turned up for a match still under the influence of alcohol.
Captain Ricky Ponting and opening batsman Matthew Hayden have been included after they returned home injured from the tour of the West Indies.
Ponting had surgery, while Hayden underwent an extensive rehabilitation programme, with both missing the recent one-day series in Darwin.
Leg-spinner Bryce McGain, who is 36, and off-spinner Jason Krejza have been picked to replace the now retired Stuart MacGill as the frontline spinners on the four-test tour of the country, whose pitches traditionally favour spin.
Ricky Ponting (captain), Michael Clarke (vice-captain), Doug Bollinger, Stuart Clark, Brad Haddin, Matthew Hayden, Michael Hussey, Phil Jaques, Mitchell Johnson, Simon Katich, Jason Krejza, Brett Lee, Bryce McGain, Peter Siddle, Shane Watson.