The Oshiwara Police said they detained Anuj on Saturday as the prime suspect in his father's murder.
Arun Tikku, a 62-year-old Ghaziabad businessman, was stabbed to death in his flat at Samarth Angan Society in Lokhandwala.
Arun had reportedly come to Mumbai to meet Anuj and convince him to join family business.
The father-son also had arguments over Anuj renting out one of the rooms in his flat to a person identified as Manoj Palande, said police.
According to his neighbours, two men, who claimed to be tenants at Arun's flat, managed to flee the crime scene before the cops arrived.
The police said they suspect Anuj killed his father with the help of a friend.
Anuj is a popular face in the advertising agency and has done small roles in films like No One Killed Jessica, Rab Ne Bana Di Jodi and Dev D.