"This has got nothing to do with who will be the successor. These are his (Sukhtankar) personal reasons. He requested that he be allowed to leave," he added.
In a regulatory filing last week, the bank announced Sukthankar's resignation without citing any reasons.
"We hereby inform you that Paresh Sukthankar has tendered his resignation as Deputy Managing Director of the bank, to be effective 90 days from the close of business hours of today (Friday)," the filing said.
Noting that the bank's board will decide on a replacement for Sukthankar in the next 10 to 15 days, Puri said: "There will no longer be a deputy MD's post at HDFC Bank."
He also noted that HDFC Bank is well capitalised and not dependent on any one individual.
"We have a split between risk and business and no one person can take a decision," the CEO said.
Sukthankar currently oversees the bank's credit, finance and human resources functions.
Last month, HDFC Bank reported a 18.2 per cent increase in its net profit at Rs 4,601.4 crore for the first quarter ending June, as compared to Rs 3,893.84 crore in the same period a year ago.
The HDFC Bank stock closed on Monday at Rs 2,090.65 a share, down Rs 24.35, or by 1.15 per cent, on its previous close on the BSE.