Forex traders said market participants are concerned that the sharp rise in coronavirus cases, could weigh on the economy.
The rupee opened weak at 76.32 at the interbank forex market and then fell further to 76.43, down 15 paise over its last close.
The rupee had settled at 76.28 against the US dollar on Thursday.
Forex market was closed on April 10 on account of Good Friday.
"Risk appetite remained weak as coronavirus fresh cases and death toll rose in the United States and back in India," Reliance Securities said in a research note.
Moreover, investors are also awaiting cues from CPI dada for March and the minutes of the Monetary Policy Committee's latest meeting scheduled to be released later in the day.
The number of deaths around the world linked to the new coronavirus has crossed over 114,000. In India, more than 9,000 coronavirus cases have been reported so far.
Brent crude futures, the global oil benchmark, rose 4.19 per cent to USD 32.80 per barrel.
Foreign institutional investors (FIIs) were net buyers in the capital markets, as they bought shares worth Rs 1,737.62 crore on Thursday, as per provisional data.
Domestic bourses opened on a weak note with benchmark indices Sensex trading 619.14 points down at 30,540.48 and Nifty lower by 159.90 points at 8,952.00.
The dollar index, which gauges the greenback's strength against a basket of six currencies, fell by 0.08 per cent to 99.40. DRR DRRDRR