Dutt was convicted in November and sentenced on July 31 to six years in prison by a Mumbai court for illegally possessing three automatic rifles and a pistol.
He was acquitted of more serious terrorism charges relating to the bombings.
He is currently appealing the sentence in the Supreme Court.
The loss of Dutt's work on two unfinished films would have cost the film industry millions of dollars. It was unclear how Dutt's bail would affect the films' status.
Dutt's case was part of the Mumbai bombings trial, which dragged on for 12 years and saw more than 100 people convicted, 686 witnesses and 13,000 pages of testimony.
The series of bombings on March 12, 1993, killed 257 people.
A dozen people were sentenced to death, while 20 others face life sentences.
More than 50 others were sentenced to between three and 14 years in jail.