The move is part of a company decision to close 70 branches across the UK.
The High Street office will close on June 1 next year.
TSB say there has been a major reduction in customer visits in the last twoyears.
The company has said that everyone employed at Melton has been offered a new role and that the business can accommodate all impacted staff with a variety of options.
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It added that customers would have the option to carry out everyday banking services at the Post Office and access cash there and the nearby ATM.
A TSB spokesperson said: “We have not taken the decision to close our Melton Mowbray branch lightly, but we have to respond to declining branch use and increasing numbers of customers switching to digital banking services.
“Customer transactions at the branch have fallen by 47 per cent since January 2019 and we see no prospect of branch transactions returning to pre-Covid levels.
“The closest Post Office is located 0.6 miles from the Melton Mowbray branch and the nearest free to use ATM is under 0.1 miles away.”
TSB had 475 branches around 12 months ago but the current round of closures will reduce that to 220.
The UK financial industry has seen a major trend towards the closure of branches, mainly due to the growth of online banking with 120 having been closed just since October.