All-rounder Pandya was vice-captain of the Rohit Sharma-led India team, who won the T20 World Cup, beating South Africa in the final last month.
Rohit, along with batting stalwart Virat Kohli, quit T20 Internationals after the victory in Bridgetown creating a leadership void.
Rohit will lead the team in the 50-overs leg of the tour next month featuring three one-dayers in Colombo.
Top-order batter Shubman Gill, who led a second-string India team in a five-match T20I series in Zimbabwe soon after the T20 World Cup, has been named vice-captain in both the squads.
Both Suryakumar Yadav and Pandya have been left out of the one-day squad in Sri Lanka.
While the BCCI seldom explains team selection, media reports said both players have been rested to help manage their workload.
The Sri Lanka tour will also mark the beginning of Gautam Gambhir's tenure as India's head coach having replaced Rahul Dravid in the job.
T20I Squad:
Suryakumar Yadav (captain), Ꮪhubman Gill, Yashasvi Jaiswal, Rinku Singh, Riyan Parag, Rishabh Pant, Sanju Samson, Hardik Pandya, Shivam Dube, Axar Patel, Washington Sundar, Ravi Bishnoi, Arshdeep Singh, Khaleel Ahmed, Mohammed Siraj
ODI Squad:
Rohit Sharma (Captain), Ꮪhubman Gill, Virat Kohli, KL Rahul, Rishabh Pant, Shreyas Iyer, Shivam Dube, Kuldeep Yadav, Mohammed Siraj, Washington Sundar, Arshdeep Singh, Riyan Parag, Axar Patel, Khaleel Ahmed, Harshit Rana
