Masks have been mandatory since July, but Aldi has now committed to refusing entrance unless someone is medically exempt, the store has also reminded people to shop alone if they can.
For a limited period, Aldi - which has branches in Peterborough at Hampton, Bretton, Stanground and Maskew Avenue - will be providing customers with a face mask if they forget to bring one.
Giles Hurley, Chief Executive Officer at Aldi UK said: "The safety of our colleagues and customers is our number one priority. Wearing a mask is mandatory for everyone that shops at Aldi, except for the small number of people who have a medical exemption."
The new rules follows those from the likes of Tesco, Asda, Waitrose, Sainsbury's and Morrisons, who have also introduced the measures.
In a statement released by Tesco, they said: "To protect our customers and colleagues, we won't let anyone into our stores who is not wearing a face covering, unless they are exempt in line with government guidance.
"Our colleagues are working hard in difficult circumstances to make sure everyone can get what they need, and we'd ask everyone to please be kind, patient and respectful as we all work to keep each other safe."