The 35-year-old star had portrayed the role of a drug-addict rockstar called Tommy Singh in the Abhishek Chaubey-directed film.
Tweeting his congratulation for his co-stars Alia Bhatt, who was adjudged best actress and best male debut winner Diljit Dosanjh, he wrote, "Congratulations to @aliaa08 and @diljitdosanjh for the much deserved awards. Here's to cinema with content. Say no to drugs. #whosthegabru".
Shahid also extended his gratitude to director and the writer of the movie.
"Thank you Abhishek Chaubey and Sudip Sharma for conceiving Tommy Singh. The Filmfare trophy belongs to you first. #drugsdimadi #whosthegabru," he wrote.
Shahid shared the award with actor Manoj Bajpayee, who won it for "Aligarh" at the 62nd Jio Filmfare Awards on Saturday.
Shahid will be next seen in "Rangoon", in which he stars alongside Kangana Ranaut and Saif Ali Khan. The Vishal Bhardwaj-directed film releases on February 24.