Shastri did not leave with the Sri Lanka-bound squad as he was tied up with media commitments in the ongoing Ashes Test series between Australia and England.
The former India captain had informed the Board of Control for Cricket in India in advance about his media commitments in England.
He is expected to be in charge of team management until the BCCI names a new head coach, a post left vacant post the departure of Duncan Fletcher.
He missed the recent series in Zimbabwe for the same reason and arrives in Colombo amid India's three-day warm-up game against Sri Lanka Board President's XI.
India will play three Test matches in Sri Lanka.
Image: Ravi Shastri