Asaram, 75, was arrested in August on charges of sexually assaulting a minor girl and has been in prison at Jodhpur in Rajasthan since then.
"We have registered two complaints, one against Asaram and another against Narayan Sai of sexual assault, illegal confinement and other charges," Surat Police Commissioner Rakesh Asthana said today.
"The victims are two sisters," he said.
The complaint against Narayan Sai has been registered at Jhangirpura police station in Surat, while the one against his father Asaram has been transferred to Ahmedabad as the alleged incident happened there, Asthana said.
The police will question Narayan Sai in connection with the complaint shortly, he said.
The older sister in her complaint is understood to have accused Asaram of sexual assault, while the younger one filed a complaint against his son. The incidents reportedly happened between 2001 and 2006.