"Some of our stores might not have all of their usual products available, and we would like to say sorry to our members and customers if this is the case in their local store," they said.
Cyber criminals behind the attack claim to have the private information of 20 million people who signed up to Co-op's membership scheme, but the firm has not confirmed that number.
The company said in April it had seen 22% growth in its active membership base to reach 6.2 million-member owners in 2024.
It has told customers visiting its website that it believes only members' personal data such as names, contact details and dates of birth - not bank details, transaction information, or passwords - have been extracted.
Aside from the issues impacting deliveries, some shoppers have been unable to pay by card or contactless at Co-op shops since Monday - something the supermarket chain says is the case for a "small number" of its 2,300 stores.
"The majority of these have been already addressed and we expect the remaining stores to be fully addressed during the course of today," a Co-op spokesperson said.