Certified by the Forest Stewardship Council, the packaging is made from more than 90% recycled cardboard and features a thin plastic liner inside to protect the pods.
The cardboard boxes can be disposed of in standard household recycling bins after use.
They are expected to save 252t of plastic a year and more than four million pieces of plastic across eight lines.
Tesco said that more than 24 million people in the UK regularly buy laundry products.
Of these, more than 38% usually choose pods, compared with 28% who prefer powder detergent and 34% who opt for liquid or gel.
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Tesco Group quality director Sarah Bradbury said: “Customers are focused on getting great value right now, but we know that they still want to choose products that use less or no plastic in their packaging.
“This is one of many changes we’re making to reduce unnecessary plastic from products right across our stores.”
The transition to cardboard packaging is in line with Tesco’s 4Rs packaging strategy to reduce its use of plastic waste.
Launched in 2019, the strategy aims to remove plastic where possible and reduce it where it cannot be removed, as well as look into ways to reuse more and recycle what is left.
Tesco claims to have removed 1.8 billion pieces of plastic and reduced its packaging by more than 10,000t since the 4Rs scheme was launched.
In addition to replacing plastic, Tesco has launched larger packs of pods for its bio, non-bio and scented product ranges.
In September last year, the retailer also launched a trial of cardboard box-free toothpaste in an effort to eliminate unnecessary toothpaste packaging.
The trial involved major toothpaste brands such as Colgate, Oral B, Sensodyne, Aquafresh and Corsadyl.