The bank's stock fell 0.33 percent to Rs 1,796.25 in early trading, Moneycontrol reported.
Rajiv Kumar succeeds Atanu Chakraborty, whose tenure as part-time chairman concluded after completing the maximum term permitted under banking regulations.
A former Finance Secretary and Chief Election Commissioner of India, Kumar brings decades of experience in public administration, economic policy and financial governance.
His appointment is expected to strengthen HDFC Bank's board oversight and corporate governance as the lender continues to expand its operations following its merger with HDFC Ltd.
The appointment is subject to the applicable regulatory approvals and is seen as part of the bank's planned leadership transition at the board level.