Dhawan suffered the injury after being hit by a Pat Cummins' delivery during his 109-ball 117 knock against Australia.
Pant, who was initially ignored for Dinesh Karthik when the 15-member squad was picked, has been named as his standby and is expected to fly in to England as cover.
"Shikhar will be in a plaster for a couple of weeks, we'll assess and see. Hopefully he'll be available for the later half and the semi-finals. He's motivated, we wanted to keep him back," Kohli said after the tie against the Kiwis was called off.
This was the fourth such game in the ongoing tournament that has not yielded any result.
So far, the South Africa-West Indies, Sri Lanka-Pakistan and Sri Lanka-Bangladesh games have all been washouts.
The ICC has said in a statement that it will be a logistical mayhem to keep reserve days for games in the group stage.
"Sensible decision to not play, given the outfield wasn't fully fit. One point not a bad thing for sides that have won all their games so far. So we'll take it," said Kohli.
India next take on arch-rival Pakistan which is always a big-ticket clash on Sunday.
"For Sunday, we know we're there when it comes to the mindset...just about going out there and having a game plan, executing it. As soon as you enter the field, it's calm and relaxed. The atmosphere from the outside, for the first time, it's a bit intimidating, but we'll look to execute well," said Kohli.
"It's been competitive for years, it's a marquee event all over the world, honour to be a part of the big game. Brings out the best in all of us," Kohli said.
The no result meant New Zealand (7 points) stay on top while India (5 points) edge ahead of England (4 points) to the third spot with Australia (6 points) staying second.
The Kiwis are yet to lose a game with three wins before this, while Virat Kohli and Co. have beaten South Africa and Australia to start their campaign on a high.