Explosives experts from the elite British regiment managed to blow open three safes without destroying 3.5 million marks stored inside and also seized other vital evidence.
Last year's mission in the southern Bosnian town Mostar was reportedly authorised by British commanders.
It was believed that the money-laundering operation was funding a plot to set up a breakaway Bosnian Croat state.
Deputy commander of the Nato-led Stabilisation Force (S-For), Major General Richard Dannatt, of the Green Howards Regiment gave the mission the go ahead, according to the Times newspaper.
Racketeering claims
The details were disclosed in a new regimental history of the Green Howards by Colonel Geoffrey Powell and his son, Brigadier John Powell.
General Dannatt was said to have called up the SAS men after he was unable to get evidence of racketeering claims.
French and German S-For troops guarded the town while the SAS approached the bank.
With only one security guard offering no resistance on the door, the soldiers got inside and blew open the safes, seizing the cash inside.
Plot stopped
They also accessed evidence stored on computers attached to a wall without demolishing the whole wall.
The cash, computers and documents reportedly provided enough evidence to end the operations of the local mafia and put a stop to the breakaway plot.
The Ministry of Defence refused to comment on the role of the SAS, but confirmed that the operation did take place.
"The incident is correct but obviously we won't discuss any details," a spokeswoman said.