The accused, identified as Ravinder Ahlawat, also works as a documentary producer and owns an acting school in Lajpat Nagar area, police said.
The incident was reported last month after which he went absconding. He was finally arrested on Wednesday after he arrived in Delhi, a senior police official said.
In her complaint, the girl told the police that Ahlawat molested her in the pretext of giving her acting lessons and also offered her roles in documentaries and ad-films.
The girl also told the police that when she resisted, Ahlawat allegedly threatened to dismiss her from his group. She had joined Ahlawat's group as a child actor a few years ago, the official said.
She further alleged that Ahlawat also asked for sexual favour for a promised role as a child artiste in a Bollywood movie, he said.
Ahlawat has been booked under relevant sections of IPC and Protection of Children from Sexual Offences (POCSO) Act, the official added.