He is playing his first tournament since suffering serious injuries in a car accident in December 2022 that kept him out of last year's IPL as well as the 50-overs World Cup in India
The BCCI said Sundar had a finger injury while Khan fractured his thumb while fielding in a warm-up match last week.
Gill sustained a developing stress reaction on his left leg during India's World Test Championship final defeat by New Zealand last month and had returned home.
Selectors called up batsmen Prithvi Shaw and Suryakumar Yadav, who are part of a second-string Indian squad currently playing a Twenty20 series in Sri Lanka, as replacements.
Wicketkeeper Rishabh Pant has linked up with the squad having recovered from COVID-19 while bowling coach Bharat Arun, Wriddhiman Saha and Abhimanyu Easwaran completed isolation before the series opener at Nottingham on Aug 4.