A spokesman for the selection committee said on Wednesday the paceman was being rested because of the amount of cricket he played on the recent tour of Australia [ Images ].
Malinga, who also has a lingering knee problem, won the man of the series award in Sri Lanka's 2-1 victory over Australia in the one-day internationals.
The selectors named four fast bowlers in their 16-man squad for the first Test -- Dammika Prasad, Dilhara Fernando, Thilan Thushara and Suranga Lakmal.
Sri Lanka will be without spinner Muttiah Muralitharan [ Images ] who retired from Tests in June with a world record haul of 800 wickets.
Squad:Kumar Sangakkara [ Images ] (captain), Mahela Jayawardene [ Images ], Tillakaratne Dilshan [ Images ], Tharanga Paranavitana [ Images ], Thilan Samaraweera [ Images ], Angelo Mathews [ Images ], Prasanna Jayawardene [ Images ], Thilina Kandamby, Ajantha Mendis [ Images ], Suraj Randiv [ Images ], Rangana Herath [ Images ], Kaushal Silva, Dammika Prasad, Dilhara Fernando, Thilan Thushara, Suranga Lakmal.