"He (Chandimal) was down with flu, but today it got worse and he was taken to hospital," Jayasuriya told AFP. "He is down with pneumonia and will not be able to play the first Test starting on Wednesday."
Jayasuriya said Chandimal's health would be monitored before a call is taken on his availability for the second Test.
Chandimal was named as skipper of the Test squad last week after Angelo Mathews quit following a humiliating 3-2 defeat in the one-day international series against Zimbabwe.
Herath, 39, took 11 wickets in the one-off Test against Zimbabwe with his left-arm spin to jump to the second place in world rankings behind India's Ravindra Jadeja.
India and Sri Lanka will play three Tests, five one-day internationals and one T20 in their first series involving all three formats of the game in eight years.