The government brought in the charge on 5 October to help reduce the amount of plastic waste.
Tesco declined to say how many 5p bags had been bought but said it was down 78% on the month before the charge, the Daily Telegraph reports.
The chain is to give the proceeds from plastic bag sales to charity.
The number of carriers bags given out by seven major supermarkets in England rose by 200 million in 2014 to exceed 7.6 billion - the equivalent of 140 per person and amounting to 61,000 tonnes in total.
Tesco's market share suggests it is likely to have handed out in excess of two billion single-use bags in 2014.
The supermarket said it had also seen a 50% increase in the amount of shoppers opting for "bagless" online deliveries.
Rebecca Shelley, Tesco's communications director, said the charge had "clearly had a huge impact" and the company was on target to donate Â£30m to charity over the year.
Marks and Spencer introduced a 5p charge on food carrier bags in 2008, which saw a reduction of 75% in usage and raised more than Â£10m for good causes.
A spokeswoman said since the legislation in October, the firm has seen a further reduction of 18% in usage.
"In clothing, since the legislation was introduced, we have seen a reduction of around 50% on clothing bags usage," she added.
England was the last part of the UK to adopt the 5p levy following successful schemes in Scotland, Wales and Northern Ireland.
The British Retail Consortium said the number of carrier bags now used by UK shoppers indicated there had been a significant reduction.
"Nevertheless, we must not let an obsessions with carrier bags get in the way of the wider and more important green goals on which retailers are working incredibly hard and making significant progress including reducing packaging, carbon emissions, food waste and waste to landfill," a spokesman said.
Environment Minister Rory Stewart told the Telegraph that reducing the number of carrier bags used "is a small but vital step in reducing plastic waste".
The number of plastic bags taken home by shoppers at Tesco stores in England has dropped by almost 80% since a 5p levy was introduced, data suggests.