The packaging is known as the 'GreenBottle', because it is easier to recycle and is biodegradable, and requires less energy to manufacture than a plastic bottle.
The outer shell is made from recycled paper, which can be recycled, and the inner liner prevents liquid from contaminating the paper outer.
Asda has been trialling the two-litre containers and will now stock them in its Lowestoft store, as part of plans to cut the amount of packaging in its stores and increase the amount that can be recycled.
The milk is supplied by local dairy Marybelle and bears the Marybelle and GreenBottle brands.
Chris Brown, head of ethical and sustainable sourcing at Asda, said: "Milk is one of our highest- selling products and, as such, we have a responsibility to develop alternative packaging, making it easier for our customers to go green and to help them recycle at home."
GreenBottle is run by Simon King and the product was designed by John-Paul Grogan.
King said: "We are delighted to be distributing the GreenBottle through Asda, who have been incredibly supportive. Our partnership is a perfect example of how environmentally friendly products can be taken to the mainstream."