The permission was granted by designated judge P D Kode on a plea made by Sanjay's lawyer Farhana Shah.
Sanjay, who is the brand ambassador of the foundation set up in the memory of his mother, would leave for the US tomorrow and return on April 21, his lawyer told.
He is scheduled to visit Chicago, Los Angeles, San Francisco and New York where fund-raising programmes are being organised for the welfare of cancer patients.
The actor will also be meeting his daughter Trishala who is staying with her maternal grandparents in the US.
However, the judge warned Sanjay to refrain from establishing any contact with the co-accused and also asked him to appear before the court within 24 hours if it was necessary. Sanjay has been asked to keep his lawyer present in the court during his absence.
The actor is facing charges of possessing an AK-56 rifle supplied by extradited underworld don Abu Salem before the 1993 Mumbai blasts and later disposing of it with the help of his friends. However, the actor denied the charges and the witnesses also did not support the prosecution.
The court is currently preparing to give its verdict in the bomb blast case in which the accused are facing the charge of being responsible for a chain of blasts at 13 prime locations in the city on March 12, 1993, allegedly at the behest of underworld don Dawood Ibrahim.