The PIL by former JNUSU President Aishe Ghosh sought urgent hearing before a bench of Chief Justice D K Upadhyaya and Justice Tejas Karia.
The senior counsel of the petitioner said that policemen were roaming with mobiles and cameras at the protest site, which, they claim, was breaking the morale of the protesting students.
She claimed that the police's conduct was in flagrant violation of the fundamental right to privacy of the protesters.
After the senior counsel urged the court to list the PIL for an urgent hearing, Chief Justice Upadhyaya scheduled it for Monday.
"We are preponing it (from Wednesday when PILs are heard). Come on Monday," Chief Justice Upadhyaya said.
The Cockroach Janta Party has been holding a protest for over 26 days demanding Union Education Minister Dharmendra Pradhan's resignation over alleged irregularities in the NEET-UG examination.
Activist Sonam Wangchuk joined the agitation on June 28 and has been on an indefinite fast since then.
The PIL, filed through lawyer Subhash Chandran KR, seeks a declaration that "continuous and intrusive mass surveillance" of peaceful protesters is constitutionally impermissible, disproportionate, and cannot be justified under the guise of maintaining public order or national security.
It seeks a direction to the authorities to immediately suspend the mass photography, videography, and surveillance at Jantar Mantar until there is a "proximate, real, and imminent threat to public order" justifying such measures.
"The petitioner has in her possession photographs depicting the permanent surveillance tower and the continuous photography and videography undertaken by police personnel, which demonstrate the pervasive and intrusive nature of the surveillance being carried out by the respondents," the plea said.
"The surveillance is indiscriminate in nature, extending to every individual present at the protest site irrespective of any suspicion of unlawful conduct and encompassing not merely the public acts of protest but also the ordinary incidents of daily life, including eating, resting, seeking medical assistance, and other personal activities," the plea argued.
