The SIB had served notice to Singh to appear before it for questioning in the scam after which he was arrested, official sources said.
Singh, who was minister in the Maywati government, had later joined the BJP and also contested the recent Assembly election on its ticket.
According to official sources, Singh, as well as the names of some other BSP ministers have come to light on the basis of interrogation of the officials of the LACCFED, a construction agency.
Sources said an executive engineer of LACCFED, Dinesh Kumar Sahu, also accused in the scam, had alleged that Singh was given Rs five crore as cut money in advance from the department's account in return for getting a contract of construction of Labour Adda (shelter for labourers) across the state in 2010.
The former minister did not return the money even after the work could not be allotted to LACCFED, Sahu said during interrogation.
Another minister in the Maywati government, Rakesh Dhar Tripathi, was also questioned by SIB a few days ago on a similar allegation. Tripathi had however denied the allegations.