The film directed by Sanjay Leela Bhansali has been facing protests by the Rajput organisation Karni Sena and other fringe groups over allegations that historical facts were distorted in it.
The city police yesterday took more than 100 supporters of the Karni Sena into preventive custody as they gathered to hold protests against the film at various places, an official said.
As the Republic Day preparations are also going on in the country's financial capital, the police have already issued a general alert and security personnel are on their toes to avoid any untoward incident, he said.
The police force is geared up to take action against those who try to create nuisance and take law into their hands while protesting against the release of "Padmavaat", he said.
The official said besides providing security cover outside theatres, some police personnel may also be deployed inside cinema halls, wherever required, to prevent any untoward incident.
The makers of the film had recently approached the Mumbai Police requesting measures to ensure smooth release of the movie.
The police also tightened security at the residences of Bhansali and the film's lead actor, Deepika Padukone, an official said.
A group of protesters had earlier this week torched tyres on the Sion-Panvel Highway and disrupted traffic movement on the Mumbai-Pune and Mumbai-Goa roads, he said.
The Vashi police in Navi Mumbai had also arrested at least 11 people for protesting against the film, he added.
The film, starring Deepika Padukone, Shahid Kapoor and Ranveer Singh, is based on the saga of the 13th century battle between Maharaja Ratan Singh of Mewar and Sultan Alauddin Khilji of Delhi.
The Supreme Court had last week paved the way for the nationwide release of "Padmaavat", by staying the ban on its screening in Gujarat and Rajasthan.