Right-handed opener Kaushal Silva was also omitted from the team that emerged victorious against Pakistan in the recent Test series held in the UAE.
Mathews was ruled out of the Test series against Pakistan due to a calf muscle injury.
Since making his Test debut in 2015, the 22-year-old Mendis was being seen as the best batting prospect for Sri Lanka after the retirement of Kumar Sangakkara and Mahela Jayawardene.
Mendis will miss out on a Test match after 22 consecutive appearances since his debut.
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Sri Lanka are slated to play three Tests, three ODIs and as many T20 Internationals in India.
The squad will leave for India on Wednesday.
Squad: Dinesh Chandimal (captain), Dimuth Karunaratne, Dhananjaya de Silva, Sadeera Samarawickrema, Angelo Mathews, Lahiru Thirimnne, Rangana Herath, Suranga Lakmal, Dilruwan Perera, Lahiru Gamage, Lakshan Sandakan, Vishwa Fernanado, Dasun Shanaka, Niroshan Dickwella and Roshen Silva.