New Zealand captain Kane Williamson suffered a fractured thumb in Friday's World Cup win against Bangladesh, but could return before the end of the group stage next month.
Williamson scored 78 before retiring hurt after he was hit by a throw as he ran through for a quick single.
It was his first game back after a seven-month lay-off with a knee injury.
Coach Gary Stead said Williamson will be given "every opportunity" to prove his fitness.
"Firstly, we're all feeling for Kane to have this occur after all his hard work to return from his knee injury," Stead said.
"While it's disappointing news, the initial diagnosis has given us some optimism he can still feature later in the pool play following a period of rest and rehabilitation.
"Kane is clearly a massive part of our side and a world-class player and captain - so we'll look to give him every opportunity we can to return in the tournament."
New Zealand's final game of the group stage is against Sri Lanka on 9 November. The semi-finals are scheduled for 15 and 16 November before the final on 19 November.
Batter Tom Blundell will travel to India as cover but will not officially be part of the squad, while Williamson recovers.
Williamson, 33, was a doubt for the tournament after rupturing his anterior cruciate ligament in the first game of the Indian Premier League in March, but recovered in time for New Zealand's third group stage match against Bangladesh in Chennai.
After passing his half-century, he looked in control before he was struck on the hand by a shy at the stumps.
He tried to continue but, when the pain persisted and with the game all but won, he retired hurt and an X-ray subsequently confirmed a fracture.
New Zealand are still without seamer Tim Southee because of a thumb injury suffered during a one-day international against England on 19 September that required surgery.
Before Saturday's India-Pakistan match, the Kiwis were top of the World Cup table after three wins from their three group matches so far.
Their next match is against Afghanistan in Chennai on Wednesday.
