Dhawan had sustained a "minor fracture" on his left hand in the second Test against Kiwis at Kolkata, the team said in a statement.
New Zealand says business as usual despite tour cancellation reports
His place in the team could go to Gautam Gambhir, who was drafted into the squad for the first time in two years after opener Lokesh Rahul suffered a hamstring strain during the first test win in Kanpur.
The hosts completed a 178-run victory in Kolkata on Monday to take an unassailable 2-0 lead in the three-match series.
The third test is scheduled to start in Indore from Saturday, but has been thrown into some confusion by a local media report that the Indian board (BCCI) had cancelled the remainder of the tour due to financial problems.
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