Dilshan has struggled during the past two years in the Test team, averaging a modest 34.65 and failing to score a century in his last 15 matches. His place has been taken by 31-year-old batsman Thilan Samaraweera.
Sri Lanka have also included left-hander Jehan Mubarak, who has impressed in the one-day team, and omitted opener Malinda Warnapura.
Warnapura had replaced the injured Upul Tharanga in their last series against Bangladesh.
Selectors had tried to persuade former captain Marvan Atapattu to return, requesting a face-to-face meeting earlier this week to discuss his future, but Atapattu declined the opportunity and was therefore not considered for selection.
The one new face in the squad is fast bowler Chanaka Welagedera, 26, who has produced some outstanding performances this year for various Sri Lanka development teams, including the 'A' team on their England tour.
Muttiah Muralitharan's recovery from a bicep injury is on track to be completed in time for the tour after he resumed bowling this week. The spinner needs eight more wickets to level Shane Warne's 708-wicket world record.
Sri Lanka play Australia in two Tests at Brisbane starting on November 8 and at Hobart on November 16.
Sri Lanka squad: Mahela Jayawardene (captain), Kumar Sangakkara (vice captain), Sanath Jayasuriya, Upul Tharanga, Michael Vandort, Chamara Silva, Thilan Samaraweera, Jehan Mubarak, Prasanna Jayawardene, Chaminda Vaas, Lasith Malinga, Dilhara Fernando, Farveez Maharoof, Chanaka Welagedera, Muttiah Muralitharan, Malinga Bandara