Sundar suffered a split webbing on his bowling hand during the game against Gujarat Titans.
The selectors added Kuldeep Yadav to the Indian squad.
The 22-year old Tamil Nadu all-rounder tested positive for COVID-19 in Bengaluru.
The all-rounder is also in doubt for the Twenty20 World Cup to be held later this year.
Sundar is the third player after Shubman Gill and Avesh Khan to be ruled out of the tour.
Sundar stayed away from his son as his work as an administrative officer in the Income Tax department in Chennai requires him to go to office two or three days every week.
Sundar thanked the badminton star for her 'kind words''.
Sundar made a memorable Test debut at the Gabba earlier this year.
India's 13th consecutive Test series victory at home also secured their place in the June final of the World Test Championship against New Zealand.
"I think I will accept the challenge just like our coach Ravi sir did during his playing days," says the Indian all-rounder.