Petitioner 'Maharashtra Lokarpan', a social organisation, stated that the ban at Dargah Hazrat Afzal Khan, located at the foot of the Fort, was imposed after some Hindu right-wing organisations threatened to demolish the structure.
The tomb was built in 1659, after Maratha king Shivaji killed Afzal Khan, a Bijapur sultanate general, near the Fort.
The tomb was later converted into Dargah. The right-wing organisations have objected to its presence near Pratapgad, which had associations with Shivaji.
Following threats by some organisations to pull it down, Maharashtra government imposed a ban entry. "Tourists are not allowed to enter the tomb area. The ban is unreasonable as the tomb is a part of Maharashtra's rich history and people should be allowed to learn more about it," the petition states.
The premises should be converted into a museum, and security in the area should be increased, it says.
The petition would be heard by the division bench of Justices A M Khanwilkar and K K Tated next week.