Dhawan had a forgettable England tour with the left-handed opener managing just 162 runs in eight innings as top-ranked India lost the Test series 1-4.
Uncapped batsman Mayank Agarwal and rookie fast bowler Mohammed Siraj were included in the 15-man team that will be led by Virat Kohli, who was rested in the recent Asia Cup 50-over tournament won by India.
The national selectors decided to rest fast bowlers Jasprit Bumrah and Bhuvneshwar Kumar due to their "recent workload", the Board of Control for Cricket in India (BCCI) said in a statement.
"Both Ishant Sharma and Hardik Pandya were not considered for selection, as they are yet to recover from their injuries," the BCCI added.
The first Test will be held in Rajkot starting October 4, with the second in Hyderabad from October 12.
The two teams will also play five one-day international and three Twenty20 matches after the Test matches.
The world's top Test side will then head to Australia for a full series starting November.
Squad: Virat Kohli (captain), KL Rahul, Prithvi Shaw, Mayank Agarwal, Cheteshwar Pujara, Ajinkya Rahane (vice-captain), Hanuma Vihari, Rishabh Pant (wicket-keeper), R Ashwin, Ravindra Jadeja, Kuldeep Yadav, Mohammed Shami, Umesh Yadav, Mohammed Siraj, Shardul Thakur.