The Shiv Sena leader shared photos of Chhota Rajan's birthday celebration on social media. Paradkar is also an accused along with Chhota Rajan in many cases.
Paradkar has been made Navi Mumbai's liaison chief by Uddhav Thackeray.
Meanwhile, the Mumbai Police have arrested six people, including an organiser of a kabaddi programme for putting up posters celebrating gangster Chhota Rajan's birthday on Saturday and Sunday.
The underworld don was deported to India after being arrested in 2015 from Bali in Indonesia. Since then, he has been lodged in Tihar jail in Delhi.
In 2018, Rajan was sentenced to life imprisonment for the murder of journalist J Dey in 2011.
(With inputs from ANI)