The second of the three one-dayers is scheduled to be played at the same venue on Tuesday. New Zealand were 13-1 from 4.2 overs in reply to Sri Lanka's 288-9 when heavy rain lashed the southern port city and wiped out the rest of the match.
Earlier, Tillakaratne Dilshan, Kumar Sangakkara and Angelo Mathews hit half-centuries to lead Sri Lanka to a big total after the home team was asked to take first strike.
Stand-in captain Kyle Mills gave the tourists a flying start when he trapped opener Dimuth Karunaratne leg-before with the first delivery of the innings.
Dilshan and Sangakkara, however, settled in to pulverise the Black Caps during a second-wicket partnership of 137.
Sangakkara made 79 off 81 balls with nine boundaries and two sixes, while Dilshan scored 81.
Left-arm spinner Anton Devcich dealt a double blow when he removed Sangakkara and former captain Mahela Jayawardene in the space of four deliveries to reduce Sri Lanka to 139-3.
But Dilshan put on 58 for the fourth