Senior Principal magistrate Martha Mutugi issued the warrant after the MP failed to appear in court for a mention of the case on Monday.
Babu is charged with assaulting a parking attendant alongside his bodyguard Fanuel Owino.
The youthful legislator was arrested on January 20 for allegedly assaulting a parking attendant at Fortis Plaza in Westlands, Nairobi.
Babu and his co-accused were also charged for using abusive language and creating a disturbance.
It was said that on the same day, he created a disturbance by pulling, shouting and threatening to harm Gichagu.
They denied the charges and were released on a personal bond of Sh20,000 each.
The hearing of the case is on March 22.