Exeter Vets4Pets is set to close on April 18, with the loss of seven jobs.
The veterinary surgery at Pets at Home on Marsh Barton is among a number of branches across the UK that have been earmarked for closure.
Customers and their pet patients are said to be devastated by the news, particularly those who have been receiving long-term care.
A message on the website reads: "We are sorry to announce the impending closure of the practice on 18th April. Please accept our sincere apologies for any distress and inconvenience this may cause.
"Letters will be sent to all clients to inform them and help with any questions regarding their on-going pet care. We will endeavor to make the process as smooth as possible for our clients."
Pets at Home announced in November last year that it was looking to close up to 30 of its vet practices under plans to overhaul the business and save money.
But it is bad news for Stone Lane Retail Park which is also set to lose its Office Outlet Store.
No other branches in Devon are thought to be affected.
No closing date has been set yet but it means that three units out of nine are set to stand empty at the retail park.
Pets at Home operates 471 vet practices through its First Opinion business and is planning to buy back 55 of the sites it runs through joint ventures as it believes it will be able to save money running them internally.
Around 300 staff could lose their jobs if the stores are shut, although Pets at Home says it hopes to find roles for employees elsewhere.
The closures come after a failed expansions of the veterinary division earlier this year.
A spokesperson for Vets4Pets said: "In line with the announcement that the business made to Joint Venture Partners, colleagues and shareholders in November of last year, we have conducted a review of our practice estate and have taken the decision to buy back into company ownership, or close a small number of practices.
"Our Exeter Marsh Barton practice is in a location that falls into the small number of businesses that we have taken the decision to close, based on our view of the longer term viability of that practice.
"We are in the process of writing to all clients of the surgery and signposting them to the nearest Vets4Pets to be able to continue to provide the best veterinary care for their pets. Importantly, we are working hard with all of our colleagues to try to offer alternative employment, still within our group.”
