Singh sent his resignation to Chief Minister Nitish Kumar late on Wednesday night, officials at the CM's office said on Thursday.
Singh told PTI on Thursday that the allegation against him of being an absconder since 1995 was true.
"Therefore, I decided to put in my papers. I was not aware of a court declaring me as an absconder in this case," he said.
"If I was aware, I would have approached the court for bail. Even my lawyers did not inform me about this," he claimed.
"After coming to know about being declared as an absconder in this case, my first duty was to resign before taking legal remedy," he said.
Singh's move comes after the Opposition Rashtriya Janata Dal demanded that he be dropped from the cabinet.
An RJD delegation led by state party chief Ramchandra Purve and Leader of the Opposition in the assembly Abdul Bari Siddiqui had on Wednesday called on Governor Devanand Konwar seeking Singh's immediate dismissal.
The RJD delegation alleged that a case had been registered against Singh over a communal speech he made in Bihar's Aurangabad district in 1992.
"Singh was declared an absconder by a court in May 1995 after he repeatedly failed to appear before it in connection with the case," they had said.
They further alleged that Singh had concealed the cases against him in the affidavit while filing his nomination from the Aurangabad assembly seat in the 2010 polls that he won on a BJP ticket.
