The Punjab National Bank (PNB), one of several state-owned lenders the government is trying to clean up, said transactions worth $1.77 billion had been made "for the benefit of a few select account holders with their apparent connivance".
It said they had occurred at a single branch in India's financial capital Mumbai.
"Based on these transactions other banks appear to have advanced money to these customers abroad," the bank said, adding that the fraud had been reported to enforcement agencies for further investigation.
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PNB did not give any further details or say which lenders were affected.
Bloomberg News reported that the value of the illegal transactions amounted to eight times the bank's net income last year.
Shares in PNB plummeted 7.45 percent on the Bombay Stock Exchange's benchmark Sensex index in late morning trade.
The news comes as the government tries to reduce the crippling debts of India's troubled lenders.
It recently announced a $32-billion recapitalisation plan for state-owned banks to help them clean up their books.
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