The NSE Nifty 50 index fell 0.76% to 15,632.10 and the S&P BSE Sensex closed down 0.68% at 52,198.51.
The Nifty Bank Index was a major drag, down 1.89%, with HDFC Bank, IndusInd, ICICI Bank and AU Small Finance Bank among the losers.
Metal and realty also ended down at 2.34% and 2.53%, respectively.
Asian Paints closed at a record high after the company's quarterly net profit more than doubled to 5.69 billion rupees ($76.29 mln), ahead of analysts' expectations of 5.21 billion rupees.
The broader Nifty Smallcap100 and Midcap100 indexes fell 1.4% each, their sharpest intraday fall in a month.
European shares bounced back from their worst day of the year on Tuesday, but Asian stocks were down, as the fast-spreading Delta variant raised fears that further lockdowns could upend global economic recovery.
Stocks on Wall Street fell as much as 2% on Monday, with the Dow posting its worst day in nine months as COVID-19 deaths increased in the United States.
(Reporting by Vishwadha Chander in Bengaluru; Editing by Shailesh Kuber)