The 31-year-old former policeman, whose five-year international career has been marred by regular injuries, suffered stiffness in his back during a practice match last week.
"It is unfortunate that Shane is having the problem before the start of the tournament and has to be ruled out of the opening match," New Zealand manager Lindsey Crocker told reporters here.
"He will be assessed on a regular basis. We will know on Tuesday if he will be able to bowl soon."
Crocker said it was too early to comment if Bond would be available for the second match against Sri Lanka on Friday.
New Zealand captain Stephen Fleming said it was "hugely disappointing" to lose his premier fast bowler at the start of the 10-nation tournament.
"All we try to do with Shane is be conservative," he said. "We are looking, of course, not at just this tournament but the tournaments down the track, in particular the World Cup.
"If we can get him through to that, it would be nice. That's the long-term aim which is part of the reason why he's not playing the first match here.
"The good thing is that maybe the injury will not affect us so much on the slow wickets in India. It gives the other bowlers a chance to grab their chances."
Bond, who has taken 87 wickets in 45 one-dayers, is regarded as one of the fastest bowlers in the contemporary game, but crippling stress fractures in his feet and back have hurt his career badly.
Bond returned New Zealand's best figures against Australia of 6-22 in the 2003 World Cup in South Africa, but missed cricket for the rest of that year with a toe injury.
He was forced to abandon the tour of England in 2004 during the second Test after failing to recover from a back injury.
A knee injury also kept him out of the game for some time after the tour of Zimbabwe in mid-2005.
The World Cup will be played in the Caribbean in March-April next year.