As of Monday, the rupee has weakened more than 9 percent against the dollar since May 22, when Fed Chairman Ben Bernanke first mentioned the possibility of slowing its asset purchasing.
Adding to the pressure, foreign investors have withdrawn $4.7 billion from Indian bond funds, and the key issue now is whether Indian equities also will see major outflows, analysts from Standard Chartered wrote in a note.
"Indian equities have been one of the largest beneficiaries of the Fed's quantitative easing program among AXJ markets [Asian markets except Japan]. As such, they are quite vulnerable to early tapering expectations," they said in a note.
And with a 6 percent weighting in the benchmark MSCI emerging markets index, weakness in Indian stocks could signal more declines for the broader index.
A weaker Indian currency could add to inflationary pressures, widen the fiscal deficit and slow capital inflows, Standard Chartered analysts warned in another note.
In the past two years, the Indian government has implemented some positive reforms, Steven O'Hanlon, chief investment officer for fixed income at ACPI, told CNBC. Inflation has fallen, he added, and the current account deficit numbers have come in slightly better.
(Read More: Indian Rupee Hits Record Low, but Some Relief Ahead)
"However, the crisis that comes today with the talk of tapering in the U.S. is a little bit early ... in terms of those reforms coming to hard numbers," he said, adding that the current account has improved somewhat and that India is doing better compared with other emerging markets where current accounts are shrinking.