The hosts have dominated the first two Tests, recording emphatic wins in both, but 34-year-old Sehwag, who has played in 104 Tests and 251 one-day internationals, has struggled for form.
He made just two and 19 in Chennai and six in his one knock in Hyderabad.
Sehwag tweeted in response to being dropped: "Will continue to work hard for my place in the team. I trust my game and am confident that, "I'll be back"."
No replacement has been named for the forthcoming matches in Mohali and Delhi and the rest of the squad remains unchanged.
India squad: MS Dhoni (captain), Murali Vijay, Sachin Tendulkar, Virat Kohli, Shikhar Dhawan, Ravindra Jadeja, Ishant Sharma, Bhuvneshwar Kumar, Harbhajan Singh, Ravichandran Ashwin, Pragyan Ojha, Ajinkya Rahane, Ashok Dinda, Cheteshwar Pujara.