Nguyen Anh Duc, its deputy permanent director, said plastic straws that come attached with products would also be removed.
Straws made from paper, rice straw, stainless steel, glass and other environment-friendly products would be sold to replace plastic straws, he added.
Saigon Co.op is the first major Vietnamese retailer to announce the decision to stop selling plastic straws. Some major supermarket chains have begun to use banana leaves to pack vegetables instead of plastic.
Vietnam disposes around 2,500 tons of plastic waste a day, according to official figures. It is the fourth largest country globally in terms of the amount of plastic waste dumped into the ocean, according to the United Nations Environment Programme.