Taxpayer-controlled RBS is now to wind down the operation instead.
The news follows an even bigger blow when Santander pulled out of an arrangement to acquire 316 RBS branches in the UK in October.
RBS, which is 82% Government-owned, had agreed in July 2010 to sell its Indian retail and commercial business to HSBC for £63 million over the tangible net asset value of the operation.
The deal had originally been expected to complete in the first half of 2011.
Neither side specified the reasons for the deal collapsing although HSBC noted that it lapsed "without all conditions required to close the transaction being satisfied".
HSBC said it "remains committed to pursuing growth in India" through its existing operations. Under chief executive Stuart Gulliver's cost-cutting plan, HSBC has been pulling back from some markets.
RBS said its Indian business was profitable with £190m of assets and generated revenue of £42m in the first nine months of this year. It operates from 31 branches and serves 400,000 customers.
RBS has been scaling back its balance sheet as it seeks to recover from its near-collapse.
But the Bank of England warned this week that banks will have to scale back further, or raise more capital, to protect themselves from likely loan losses and regulatory fines.