The 27-year-old was named test captain earlier this month after skipper Angelo Mathews stepped down following Sri Lanka's first one-day international series defeat to Zimbabwe.
The right-handed batsman then led Sri Lanka to a win in the one-off test against Zimbabwe, during which his team chased down their highest-ever fourth innings total.
Chandimal had contracted viral influenza and was recommended a rest period of three to five days on Thursday, Sri Lanka Cricket (SLC) said in a statement.
"He was hospitalised this morning when increased symptoms showed a development of Pneumonia," the board said.
"Chandimal will miss the first test against India in Galle on the 26th–30th July, and in his absence the team will be led by veteran spin master Rangana Herath."
Sri Lanka have limited-overs captain Upul Tharanga in the side, while 39-year-old Herath also lead the side last year in the absence of Mathews.
Former fast bowler Chaminda Vaas will guide the Sri Lankan pace attack for the series against India, SLC added.
(Reporting by Sudipto Ganguly in Mumbai; editing by Amlan Chakraborty and Alexander Smith)
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