The supermarket claimed it is the first major retailer to take action in this way.
Tesco will stop ordering the multipacks from 2 March, adding it is working with its suppliers to come up with alternatives.
About 180,000 multipacks of soup, baked beans, tomatoes and such like are sold each day and are among the store’s most frequently bought items.
"We are removing all unnecessary and non-recyclable plastic from Tesco," said Dave Lewis, chief executive.
Greenpeace has been a fierce critic of the use of plastic packaging by supermarkets and welcomed Tesco’s decision, especially as it puts pressure on its suppliers.
The environmental group estimates that supermarkets used 903,000 tonnes of single-use plastic in 2018, a 2% increase.
Clive Black, a retail analyst at broker Shore Capital, said the Tesco initiative is part of a wider aspiration to take one billion plastic items out of its business this year.
“The decision by Tesco, notably to us, includes proprietary brands (PBs), so the likes Heinz soups and John West tuna, as opposed to only its own private label (PL), so making a difference to its grocery offer versus its peers.”
“From a price and promotional value proposition, Tesco UK has said it will continue to issue offers, such as multi-buys, but without the outer wrapping.
“It will be interesting to see if this stance is deemed popular by the shopper, as it requires a modicum of more shopping.”
Shore Capital has a buy rating on Tesco shares and a 243p target price.
Shares rose 1.3% to 246.2p.