The bank revealed its decision to shut more High Street banks in the county in letters to customers.
Both branches will close on August 26, with the next closest Barclays branches Leominster for Ludlow and Telford for Bridgnorth
Barclays said 80 per cent of its customers in the two towns already used different ways to bank and that everyday transactions could be completed in the local post offices.
However, Ludlow county councillor Andy Boddington said banks had a wider importance to towns.
"Having banks is one of the things that makes Ludlow town centre tick. People come to bank and then they shop," he said.
"Many people, particularly older people, are not comfortable with digital technology. There are also many businesses in Ludlow that deal with cash."
"The closure of Barclays is yet another nail in the coffin of our high streets. Ludlow town centre is resilient. It has survived the trend towards shopping online. It survived the pandemic. But how many more blows can it take?"
A Barclays spokesperson said: “The decision to close a branch is never an easy one. However, customers are increasingly using alternatives to branches to do their banking. As a result, we are seeing a sustained fall in branch visits across the UK.
“This is reflected at Ludlow and Bridgnorth branches where 80 and 83 per cent of our customers at the branches are already using different ways to bank.
"In total, 251 regular Ludlow customers and 113 regular Bridgnorth customers use these branches exclusively for their banking and do not interact with us in other ways. We will work with our customers and provide alternative options to ensure they can continue to manage their money and receive financial expertise when required.”
The spokesperson said customers were free to use ATMs in Ludlow and Bridgnorth and said everyday transactions could be completed at any post office, with the closest located in Tower Street, Ludlow, and High Street, Bridgnorth
"The role of the physical branch is evolving, with fewer than 10 per cent of transactions now taking place inside a branch," they added.
"We will be engaging with local businesses and the wider community to discuss the alternative ways customers will be able to undertake their banking locally and will be offering virtual ‘tea and teach’ sessions for customers wishing to explore digital banking and other alternatives to branch-based banking.
"We will still have an active presence in the community via new and alternative touch points."