The local unit had closed at 74.99 a dollar on Thursday.
Forex traders attributed the rupee's weakness to stronger US dollar against its key rival currencies.
The dollar index, which measures the American currency's strength against a basket of major currencies, was at 96.8640, up 0.17 per cent.
Meanwhile, global crude oil benchmark Brent Futures declined 0.78 per cent to trade at USD 42.02 per barrel.
On the equity market front, Indian benchmark indices Sensex and Nifty were marginally lower in early trade.
Foreign investors bought equities worth Rs 212.77 crore on Thursday, exchange data showed. MKJ ANS ANS