The left-hander was hit twice by New Zealand pace spearhead Trent Boult during India's second innings on Day 3 of the second Test in Kolkata.
Karnataka batsman Karun Nair was named as his replacement.
Dhawan, who was taken to a hospital in Kolkata for scans, has been recommended 15 days rest, which effectively rules him out of the third and last Test, starting October 8.
"Dhawan has been ruled out of the third Test of the Paytm Test series against New Zealand after he sustained a minor fracture on his left hand," BCCI secretary Ajay Shirke said in a media release, after India posted a 178-run win over New Zealand in the second Test in Kolkata and took an unassailable 2-0 lead in three-Test series.
"A very minor fracture has occurred and he has been recommended 15 days rest, which effectively rules him out of the next Test," said India's media manager after the match.
The left-handed opener on Sunday took blows on his bottom hand thumb twice with the ball rising awkwardly. He survived some anxious moments, managing to open his account after 14 balls, and the swollen thumb had to be taped and was later rushed to a hospital for x-ray.
He did not take the field when New Zealand were batting in the second innings and was replaced by substitute fielder Gautam Gambhir, who will take his place as the opener in the third Test.
Veteran Gambhir made a comeback to the Indian Test squad after two years in place of the injured KL Rahul, who sustained a hamstring injury during the first Test in Kanpur and was subsequently ruled out of the series.
IMAGE: Shikhar Dhawan bats during the second Test in Kolkata
Photograph: BCCI
Why Kohli believes India can hold on to No. 1 ranking
PHOTOS: India crush New Zealand to reclaim top ranking
India dislodge Pakistan from perch, take No.1 spot in ICC Test rankings
BCCI open to DRS only if it's close to perfection: Thakur
BIG jolt for BCCI as Lodha panel asks banks to halt disbursements