The arrests came after a group of striking students confined FTII Director Prashant Pathrabe and other staffers in his office for eight hours, and vandalised office furniture and fittings on Monday.
The students, numbering more than two dozen, were protesting against what they alleged was "irrational and unjustified" pro-rata course project assessment of the 2008 batch.
"The students shouted slogans in his office, physically prevented him and other staffers from leaving the office, snapped communication lines and damaged office computers. They demanded that he should immediately cancel the project assessment or they would not release them," an official said on Wednesday.
The students also formed a human chain to stop Pathrabe from stepping out, threw rapid fire questions at him repeatedly, shouted slogans like "PM Narendra Modi & Arun Jaitley murdabad" and caused mental torture to the officials.
Following the incident, Pathrabe lodged a complaint with Deccan Police Station late on Tuesday.
The police swung into action by registering a FIR against 15 students and sent teams to the campus at around 12.45 a.m.
In the action, at least five were picked up and arrested on various charges, including rioting under the Indian Penal Code, and other non-bailable offences, around 2 a.m., the police official said.
They will be produced before a magistrate later today.
Police teams are on the lookout for the others, including at least three women, who they believe maybe hiding in or around the FTII campus.
The police crackdown caps the 72 day old agitation in which a section of the students are opposing the appointment of BJP member and TV actor Gajendra Chauhan as FTII chairman.
Last week Congress vice-president Rahul Gandhi visited the FTII and expressed solidarity with the students.
Later, he took a delegation of the FTII students to meet President Pranab Mukherjee.