Officers were called to the Bank of Scotland branch in Mitchelston Industrial Estate in Kirkcaldy just before 13:30.
Nobody was injured in the incident, but people in nearby premises, including shops and schools, were kept inside the buildings as a precaution.
A Bank of Scotland spokeswoman said a four-figure sum of money was stolen during the raid.
Police officers remained on the scene on Wednesday night. Officers also confirmed a bomb disposal unit was in attendance.
Supt Derek McEwan of Police Scotland said: "This is an unusual incident for Kirkcaldy and a large number of officers are currently working to ensure the area is safe, speak to those who have witnessed this robbery and return the area to normal as quickly as possible.
"Our priority was to ensure the safety and wellbeing of all members of the public in the vicinity of this incident. A number of items were found and to ensure their safe removal, specialists from the military Explosive Ordnance Device Unit attended and examined them.
"These items are in the process of being removed but did not pose a risk to the public.
"A decision was also made to prevent the public from leaving nearby shop premises and schools for a short period of time, however this was done to ensure their safety.
"There were no threats directed at these premises or the public within, and this was merely a precaution until we could satisfy ourselves the area was safe."
A Bank of Scotland spokeswoman said: "We can confirm there was an incident earlier today at our Kirkcaldy branch. No one was injured, but the individual escaped with a sum of money.
"If anyone has any information which could help the investigation, please contact the police immediately."
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