New Zealand, sent into bat after Sri Lanka won the toss, were 145-3 after 28.5 overs when rain disrupted play for the third time.
Players were still off the field at the scheduled end of the innings and there was no word from the umpires whether they believed play would resume.
For New Zealand Martin Guptill was not out 66, while for Sri Lanka Angelo Mathews had three for 21.
The seven-match series is tied 1-1.