Singh, however, cannot come out of jail for now as he is facing other cases as well.
Additional District and Sessions Judge-I Sachchidanand Singh passed the order on a bail application moved by the MLA from Mokama last week.
Singh had allegedly made the derogatory and casteist remarks against Manjhi a few days before the latter resigned on February 20, 2015.
Manjhi had quit ahead of the trust vote due to imminent defeat.
Singh, a three-term MLA from Mokama constituency in Patna district, is currently in Beur jail in Patna.