The match will be played on Tuesday, weather permitting, as a reserve day has been kept aside for all seven matches of the series also featuring India.
A heavy thunderstorm hit the Sri Lankan capital early Monday and drenched the Premadasa stadium, where the day-night international was due to be played.
It stopped raining by noon, but another wet spell just before the scheduled start at 2:30 pm (0900 GMT) here on Monday prompted match referee Chris Broad of England to call off the game.
More inclement weather caused by the south-western monsoon has been forecast over the next few days.
The series is scheduled to run till August 29 with each team playing the other twice in the league before the final.
An outdoor practice session for the Indian team at the Sinhalese sports club was also called off on Monday due to the weather.