New Zealand were 211-5 off 46.1 overs when persistent rain worsened sufficiently for the umpires to halt play at 2:00 pm (1300 GMT) with 23 balls left in the innings.
Ross Taylor was 67 not out and Tom Latham three not out.
New Zealand captain Kane Williamson had earlier made 67 after winning the toss, with Jasprit Bumrah (1-25 off eight overs) leading a disciplined India bowling attack.
After more than four hours without play, the covers started to be removed but no sooner had an inspection been announced for 6:10 pm (1710 GMT) then fresh rain fell on the Manchester ground.
There are an additional two hours’ playing time in which to complete the match on Tuesday, although match referee David Boon can use his discretion to extend the playing hours further in he feels there is a realistic chance of achieving a result.
But a reserve day has also been scheduled for Wednesday.
The reserve day, however, will only come into operation if the minimum 20 overs-per-side match needed for a result under the Duckworth-Lewis method for rain-affected games cannot be finished on Tuesday.
In that case, the match would continue Wednesday from where it left off rather than be re-started.
If a 20 overs per side match cannot be completed on Wednesday as well, India would go through to Sunday’s final at Lord’s on the basis of having finished first to New Zealand’s fourth in the 10-team group stage.
No reserve days were scheduled for the group matches of this World Cup, which has already featured a record four washouts.
Tournament hosts England and reigning champions Australia will contest the second semi-final at Edgbaston on Thursday, with that match able to continue on to Friday if a reserve day is required.