The Co-op branch in Sumner Street, Bankside, has become the first local branch of any of the major supermarket chains to close during the COVID-19 crisis.
The Co-op has closed a number of central London stores including branches in the City of London and the West End.
"These are unprecedented times, we are committed to serving our communities, and we have had to make difficult decisions so that we can keep our colleagues safe, maintain stock levels and continue to serve our customers and members," said a Co-op spokesman.
"This means we have temporarily closed a small number of stores, which are in non-residential areas and city centres as commuters now work from home, with resources, colleagues and supplies moving to our busiest stores.
"Over 2,500 Co-op stores are open, serving communities across the UK. We thank our customers for their support and understanding as we work to serve them during this difficult time.
"We will open all this store again as soon as we can, and we thank our customers for their support as we all pull together at this difficult time."
For the latest local news and events direct to your inbox every Monday, you need our weekly email newsletter SE1 Direct.
7,000+ locals read it every week. Can you afford to miss out?
Read the latest issue before signing up