The film will see actor Ranbir Kapoor essay the role of Dutt.
"First shot taken now for Sanjay Dutt's biopic. Canning a very funny scene. Excitement in cast and crew," tweeted Hirani.
The film will also star "Masaan" actor Vicky Kaushal, who will reportedly play the role of Dutt's close friend.
Dutt and Hirani have been friends for a long time having worked together in films like "Munna Bhai MBBS", "Lage Raho Munna Bhai" and "PK".