The seven-year-old victim, who was ill, went to the clinic of Virendra Jain in New Market area along with her mother, they said.
The doctor asked her mother to wait outside and took the girl on the backside of the clinic where he allegedly molested her, the sources said.
The girl, after reaching home, narrated the incident to her mother, who informed her husband and went to the Kotwali police station to file a complaint against the doctor, the sources said.
The police station in-charge initially refused to entertain the complaint, but relented following intervention by senior police officers and protest staged by some local RSS workers, they said.
An FIR was filed against Jain and he was arrested.
The doctor was later produced in a local court which sent him in judicial custody, the sources added.