The court of Chief Judicial Magistrate at Barh in Patna district issued the arrest warrant against Singh in connection with a case registered against him under the Unlawful Activities (Prevention) Act (UAPA).
Earlier the Bihar police has issued a lookout notice against him. Officials at the state Police Headquarters said searches were being conducted to arrest Singh.
Singh was booked under Arms Act, Unlawful Activities (Prevention) Act (UAPA) Act and Explosive Act on Saturday, a day after police recovered a loaded AK-47 rifle, a hand grenade and cartridges from his ancestral house at Ladma village in Madhepura district.
On Sunday night, police searched Singh's official residence in Patna and questioned his wife and some of his henchmen to find out his whereabouts.
The absconding MLA has released two videos on the social media in which he accused the police of framing him under false charges and assured that he would surrender in four days.
Singh said the police action against him was part of political vendetta by the state government, because he was criticising it.
Singh, earlier an MLA of Bihar's ruling Janata Dal-United (JD-U), was once seen as man close to Chief Minister Nitish Kumar. They fell out ahead of the September 2015 Assembly elections, which Singh contested as an independent and won.
Singh, belonging to state's powerful Bhumihar caste, is much feared in Mokama and neighbouring areas in rural Patna. He has dozens of criminal cases, including several for murder and kidnapping, registered against him.
His wife contested the 2019 Lok Sabha polls on a Congress ticket from Munger, but lost.
( With inputs from IANS )