The court directive came after Aaradhya, who is the grandchild of acting legend Amitabh Bachchan, moved the court seeking an injunction on the media reports since she is a minor.
Abhishek and Aishwarya, who got married in 2007, welcomed their child in 2011.
Social media trolls are often seen targeting Aaradhya.
Aaradhya, who often accompanies her parents to big events even abroad, was last seen at the grand inauguration of Nita Mukesh Ambani Cultural Centre (NMACC) in Mumbai.