The rupee closed at 79.9625 per US dollar, down from 79.8650 in the previous session.
A total of 1,904 shares have advanced, 1,427 shares declined, and 148 shares were unchanged.
Barring HUL and Nestle, all Sensex shares closed with gains - with Tata Steel, IndusInd Bank, Bajaj Finance, NTPC and Tech Mahindra surging as much as 6.54 per cent.
Russian President Vladimir Putin's announcement of starting a military operation in Ukraine sent world markets into a tizzy with shares in Asia plunging into deep red.
Market participants will also look forward to re-examination of laws dealing with withholding tax on dividends.
Shares of RBL Bank shed 18.5%, after falling as much as 25% earlier in the session.
The NSE Nifty 50 index fell 1.4% to 16,745 by 0347 GMT and the benchmark S&P BSE Sensex was down 1.4% at 56,235.04.
The potentially more contagious Omicron was first reported to the WHO from South Africa on November 24.
The company's market valuation went past Rs 1 lakh crore mark and closed at Rs 1,04,438.88 crore on the BSE.
The 30-share BSE index ended 555.15 points or 0.93 per cent lower at 59,189.73. Similarly, the broader NSE Nifty tumbled 176.30 points or 0.99 per cent to 17,646.