It directed the matter to be listed for hearing on Friday.
An apex court bench of Justice Mukundakam Sharma and Justice Anil R. Dave issued notices to the central and the Uttar Pradesh governments on Jha's petition.
As senior counsel Harish Salve pressed for the stay on the ban order, Justice Sharma said they would like to hear the state government before taking any decision.
The court gave a short date as Salve submitted that any delay would further cause losses to the film as a long weekend is ahead.
"Aarakshan", starring Amitabh Bachchan, Saif Ali Khan and Deepika Padukone, deals with the sensitive issue of caste-based reservations in the Indian education system.