Prasanna, the right-arm leggie with a whipping action, had taken three wickets in a single over in his One-day debut last week against Australia.
Shaminda Eranga, another debutant who impressed in the One-day series which Sri Lanka lost 3-2, is the only other uncapped player.
He will be one in a quartet of fast bowlers short of experience who among them have played a total of just 19 Tests.
Sri Lanka will be relying heavily on the spin of Suraj Randiv and Ajantha Mendis in the absence of the experienced Lasith Malinga who no longer plays Test cricket.
The first Test begins in Galle on August 31.
Sri Lanka Squad: Tillakaratne Dilshan (C), Tharanga Paranavitana, Kumar Sangakkara, Mahela Jayewardene, Thilan Samaraweera Prasanna Jayewardene, Angelo Mathews, Suraj Randiv, Suranga Lakmal, Chanaka Welagedara, Dhammika Prasad, Shaminda Eranga, Lahiru Thirimanne, Seekkuge Prasanna and Ajantha Mendis
Sri Lanka name uncapped Prasanna, Eranga in the Test squad
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