The company claimed the closure was the result of 'changing needs of customers' following a review to ensure their branch network offers a 'sustainable service'.
The Knaresborough location is said to be one of a number of 'unsustainable and “lapsed-lease” locations' which will be closed on September 5.
Steve Fletcher, Head of Customer Banking Networks, Clydesdale Bank and Yorkshire Bank, said: “I understand this will not be welcome news for those who use this particular branch.
"These are difficult decisions but ones we must face as we try to keep up with the pace of change in the way people want to bank.
"We have to balance our investment to ensure we support demand where it is greatest, across mobile, online and branch services."
The accounts of Knaresborough customers will automatically be transferred to the Harrogate branch of the bank on James Street and services will also be accessible at Post Office counters.
Yorkshire Bank also announced the review would allow for more investment in branch technology including 100 new ATMs, each with deposit functionality, refurbishments and new Saturday opening hours.
Mr Fletcher said: “Branches remain vitally important to us, and we continue to invest in them, the services they offer and when we offer them.
"I hope that the investment we’re making in the overall quality of our branch network, the big increase in Saturday opening and the availability of other ways to bank, like local Post Office counters, will minimise the effect of this announcement for customers.”
But for Knaresborough Town Councillor, James Monaghan (Lib), the announcement is a concerning one not just for the bank's customers but for Knaresborough in general.
Coun Monaghan said: "This is disappointing news and will be a source of worry for customers who use this bank regularly.
"Getting to Harrogate isn't easy for everyone and will cause some peoploe real problems. This decision also means there will be another empty retail unit in the centre of Knaresborough."