Officers were called to the Queen Street branch after someone reported hearing glass being smashed near the bank at around 00.50am today.
Police said one of the building’s windows had been smashed.
A 36-year-old man has been arrested and remains in custody.
The bank was closed today and displayed a notice on the front of the building but a spokesman apologised and said it would reopen as soon as possible.
A spokesman for Lloyds Bank said: “We are working with the police following a security incident overnight and cannot provide any further information while this investigation is ongoing.
“We aim to reopen the branch as soon as possible and apologise to customers for any inconvenience while it remains closed.”