The decision was taken by the cabinet at a meeting chaired by Chief Minister Nitish Kumar, an official said.
"The move is to provide an opportunity to people to watch this movie, which is about one of our greatest athletes," the official said.
Directed by Rakeysh Omprakash Mehra, "Bhaag Milkha Bhaag" stars Farhan Akhtar, who plays Milkha Singh, and Sonam Kapoor.