The 36-year-old left-hander arrived on Saturday amid speculation that he would feature in the second Test against England next week.
Meanwhile, Muttiah Muralitharan and Chaminda Vaas have also been rested while seven of the eleven players who took field in the drawn Lord's Test have been included.
Sussex have also rested most of their first-choice players including Pakistan stars Mushtaq Ahmed and Rana Naved-ul-Hasan.
The visitor's seam bowlers came in for criticism for their performance during the first Test and the likes of Nuwan Zoysa and Lasith Malinga will be hoping to impress ahead of the Edgbaston Test.
They will come up against a much-changed Sussex team which will be led by seamer James Kirtley in the absence of regular skipper Chris Adams.
Sri Lanka (from): Upul Tharanga, Jehan Mubarak, Michael Vandort, Kumar Sangakkara, Mahela Jayawardene, Thilan Samaraweera, Kapugedera, Prasanna Jayawardene, Kulasekara, Nuwan Zoysa, Lasith Malinga, Malinga Bandara.