Barclay's branch on Murray Street will officially shut on December 7.
This means residents will have to travel a 16-mile round trip to access their closest branch, which will be the one located in Scarborough on St Nicholas Street.
Everyday transactions, typically carried out over branch counters (including paying in a cheque or depositing cash), can be completed at the Post Office at the town's Evron Centre on John Street.
Barclays says the decision is as a result of a fall in transactions at the Filey site, with only 115 customers using branch exclusively for their banking.
But local MP Kevin Hollinrake expressed his disappointment over Barclay's decision.
The Conservative MP for Thirsk and Malton said: "This decision by Barclays leaves many constituents without ready access to banking services locally.
"Filey, and the Thirsk and Malton constituency as a whole, contains an ageing population, many of whom do not drive, struggle with access to public transport and do not have access to the internet.
"Those who are computer literate are often hindered when using online banking services due to the poor availability of broadband in towns and villages across Thirsk and Malton.
"I understand the drive towards online and mobile banking but there are a number of concerns, including instances of fraud, which I am investigating in my role as co-Chair of the APPG on Fair Business Banking.
"I shall be meeting the Head of Corporate Relations North East for Barclays and their Community Banking Director for Yorkshire to discuss this in more detail and to ask them to keep the branch open."
Filey Town Councillor, Jacqui Houlden-Banks, echoed: "I'm aware of the decision and I'm highly against it. I feel strongly for the local people especially older people, which will find it very hard to travel to Scarborough.
"It's our last bank and if they remove the ATM machine as well it's going to be horrendous both for residents and tourists.
"I hope they'll change their mind and maybe keep the branch open for perhaps just two days a week."
Barclays, who have been sending out letters to their customers to inform them of the upcoming closure, have published a report listing the reasons behind the decision.
According to Barclays the Filey branch is closing because:
- The number of transactions has gone down in the previous 24 months, with 69 per cent of branch customers also using other ways to do their banking such as online and by telephone.
- Customers using other ways to do their banking has increased by 21 per cent since 2012
- In the past 12 months, 50 per cent of this branch's customers have been using neighbouring branches.
- The bank says only 115 customers use this branch exclusively for their banking.