A bench headed by Justice S J Mukhopadhaya asked Khan, who was sentenced to undergo five-year jail term by a trial court, to file his response within four weeks.
The state government approached the apex court against the order of Rajasthan High Court which had, on November 12 last year, stayed his 2006 conviction in the case and paved way for him to apply for a British visa.
Under British immigration rules, any person convicted for more than four years is not eligible for a visa. Since the actor was convicted for five years, he was denied visa by the UK Embassy.
The passports of Indian convicts are stamped with the word "convict."
Black buck is a protected animal and its hunting is a punishable offence.
Khan was convicted and sentenced to one-year and five-year prison terms in separate cases of poaching of two Chinkaras at Bhawad and one black buck at Ghoda Farm (Mathania) on the intervening night of September 26-27, 1998 and September 28-29, 1998 respectively.
The actor had approached the High Court in 2007 seeking a stay on his conviction by a trial court so that he could file a fresh application for a British visa.
Besides Khan, actors Saif Ali Khan, Sonali Bendre, Tabu and Neelam were accused of poaching near Jodhpur during the shooting of the film 'Hum Saath Saath Hain'.