The directives to display shop names, numbers, and their employees' names are to ensure a peaceful Yatra given the large number of participants and the potential for communal tensions.
The petition, moved by the National Loktantrik Party through its national president (executive) Mohammad Suhail, sought urgent hearing in the matter from the court.
The state Congress alleged that the BJP was trying to incite hatred between different religions and communities with such orders as it suffered a setback in the recent Lok Sabha elections.
SC bench, led by Justices Hrishikesh Roy and S.V. N Bhatti, issued an interim order on Monday after hearing a plea from the NGO, Association For Protection of Civil Rights.