A sell-out crowd of 88,000 at the Eden Gardens returned home disappointed as the weather ruined what promised to be an absorbing contest.
Sri Lanka were 102-3 after 18.2 overs after being sent in to bat when umpires Simon Taufel and Suresh Shastri ordered players off the field.
The umpires finally called off the match at 8.
30 pm (1500 GMT) when no time was left to play 20-overs-a-side, the minimum requirement to gain a result.
Veteran opener Sanath Jayasuriya was unbeaten on 63 off 61 balls and former captain Marvan Atapattu was on five when play was stopped.
Jayasuriya and opening partner Upul Tharanga hammered 23 off the first three overs before fast bowler Munaf Patel hit back with two wickets in the space of five deliveries.
Patel, returning to the Indian side after an ankle injury forced him to miss the preceding series against the West Indies, bowled Tharanga off the inside edge for 14 runs.
He then had Sri Lankan captain Mahela Jayawardene caught at mid-on for zero b