The crime came to light when the elder of the two sisters, 17, told her mother about the ordeal last week, said a police official.
The younger sister is 13 years old, he said.
When the woman confronted her husband about it, he abused her, after which she took both the girls to the Vakola police station and lodged a complaint, said senior inspector Kailashchand Avhad.
Police registered a case of sexual assault under the Protection of Children from Sexual Offences Act (POCSO) against the man.
The elder girl, who is a class XI student, told the police that her father had sexually assaulted her many times in the last two years.
He had allegedly threatened to stop paying for her education and even throw her out of the house if she complained.
In November last year, the accused tried to sexually assault her younger sister too, she told the police.
The accused was arrested on April 8 and a special court for the POCSO Act sent him in police custody till April 12, Avhad said, adding that that probe is underway.