Herath, a leading performer in the ongoing second Test between the teams in Colombo, misses out together with Mahela Jayawardene, who has yet to recover from a fractured finger.
Tillakaratne Dilshan has been included "subject to fitness" as he continues to battle a quadriceps strain, while there are maiden ODI call-ups for batsmen Angelo Perera and Kithuruwan Vithanage, and all-rounder Sachith Pathirana.
Spinners Ajantha Mendis and Akila Dananjaya, who both featured in the recent limited-overs matches against Australia, have been omitted as off-break bowler Sachithra Senanayake returns. There is also no place for seamer Suranga Lakmal.
The first two matches will take place in Hambantota on March 23 and 25.
Changes may yet be made to Sri Lanka's squad for the final game in Pallekele, which is followed by a solitary Twenty20 international.
Sri Lanka squad: Angelo Mathews (captain), Dinesh Chandimal (vice-captain), Tillakaratne Dilshan, Kushal Janith Perera, Kumar Sangakkara, Lahiru Thirimanne, Jeevan Mendis, Thisara Perera, Nuwan Kulasekara, Lasith Malinga, Sachithra Senanayake, Upul Tharanga, Kithuruwan Vithanage, Angelo Perera, Shaminda Eranga, Sachith Pathirana.