The 30-year-old, who has been struggling with his Test form in the last two years, was replaced by Thilan Samaraweera.
Dilshan, has however been kept on standby and named skipper for the A team which will tour Zimbabwe beginning October 15.
The selectors also picked 26-year-old uncapped left-arm seamer Chanaka Welegedera and leg-spinner Malinga Bandara after he was overlooked for the ongoing one-day series against England.
Veteran Sanath Jayasuriya retained his opening berth after former skipper Marvan Atapattu opted out.
Selectors had asked Atapattu to consider a return to the side last week but Atapattu declined the offer.
Ace spinner Muttiah Muralitharan, nursing a bicep injury and needing just eight wickets to level Shane Warne's world record of 708 wickets, has been named in the squad.
The first Test will be played in Brisbane from November 8 while the second will be held at Hobart (Nov 16-20).
Sri Lanka squad: Mahela Jayawardene (captain), Kumar Sangakkara, Sana